Question 1

Simplify the complex fraction by using Method II. $$\frac { \frac { 56 x ^ { 2 } + 32 x } { x - 8 } } { \frac { 4 + 7 x } { 24 - 3 x } }$$

Accepted Answer

The answer of Simplify the complex fraction by using Method...

Question 2

Write the domain of the rational function in interval notation. $$k ( x ) = \frac { x ( x + 7 ) } { x ( x - 12 ) ( x + 7 ) }$$

Accepted Answer

A)  $( - \infty , 12 ) \cup ( 12 , \infty )$ 
B)  $( - \infty , - 7 ) \cup ( - 7,0 ) \cup ( 0,12 ) \cup ( 12 , \infty )$ 
C)  $( - \infty , - 7 ) \cup ( - 7,0 ) \cup ( 0 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $( - \infty , 12 ) \cup ( 12 , \infty )$ 
B)  $( - \infty , - 7 ) \cup ( - 7,0 ) \cup ( 0,12 ) \cup ( 12 , \infty )$ 
C)  $( - \infty , - 7 ) \cup ( - 7,0 ) \cup ( 0 , \infty )$ 
D)  $( - \infty , \infty )$

Question 3

Simplify the complex fraction by using Method II. $$\frac { \frac { 2 x + 3 } { x ^ { 3 } } } { 5 x - \frac { x ^ { 2 } + 9 } { x } }$$

Accepted Answer

A)  $\frac { - 5 x ^ { 2 } - 20 } { x ^ { 2 } }$ 
B)  $\frac { \left( - x ^ { 2 } + 5 x + 9 \right) ( 2 x + 3 ) } { x ^ { 4 } }$ 
C)  $\frac { 2 x + 3 } { x ^ { 2 } ( 2 x - 3 ) ^ { 2 } }$ 
D)  $\frac { 1 } { 2 x ^ { 3 } - 3 x ^ { 2 } }$ 
A)  $\frac { - 5 x ^ { 2 } - 20 } { x ^ { 2 } }$ 
B)  $\frac { \left( - x ^ { 2 } + 5 x + 9 \right) ( 2 x + 3 ) } { x ^ { 4 } }$ 
C)  $\frac { 2 x + 3 } { x ^ { 2 } ( 2 x - 3 ) ^ { 2 } }$ 
D)  $\frac { 1 } { 2 x ^ { 3 } - 3 x ^ { 2 } }$

Question 4

Solve for b. $$h = \frac { 2 A } { B + b }$$

Accepted Answer

A)  $b = \frac { 2 A - B } { h }$ 
B)  $b = \frac { 2 A + h B } { h }$ 
C)  $b = 2 A - B$ 
D)  $b = \frac { 2 A - h B } { h }$ 
A)  $b = \frac { 2 A - B } { h }$ 
B)  $b = \frac { 2 A + h B } { h }$ 
C)  $b = 2 A - B$ 
D)  $b = \frac { 2 A - h B } { h }$

Question 5

Add or subtract as indicated and simplify if possible. $$\frac { 13 x } { - 3 x + 4 } + \frac { 7 } { - 3 x + 4 }$$

Accepted Answer

A)  $\frac { 91 x } { - 3 x + 4 }$ 
B)  $\frac { 20 x } { - 3 x + 4 }$ 
C)  $\frac { 13 x + 7 } { - 3 x + 4 }$ 
D)  $\frac { 13 x + 7 } { - 6 x + 8 }$ 
A)  $\frac { 91 x } { - 3 x + 4 }$ 
B)  $\frac { 20 x } { - 3 x + 4 }$ 
C)  $\frac { 13 x + 7 } { - 3 x + 4 }$ 
D)  $\frac { 13 x + 7 } { - 6 x + 8 }$

Question 6

Find the least common denominator (LCD). $$\frac { 10 x } { x + 10 } , \frac { 17 } { x ^ { 2 } - 100 }$$

Accepted Answer

A)  $x - 10$ 
B)  $x + 10$ 
C)  $x ^ { 2 } - 100$ 
D)  $( x + 10 ) \left( x ^ { 2 } - 100 \right)$ 
A)  $x - 10$ 
B)  $x + 10$ 
C)  $x ^ { 2 } - 100$ 
D)  $( x + 10 ) \left( x ^ { 2 } - 100 \right)$

Question 7

x varies directly as p. If x = 48 when p = 8, find x when p is 15.

Accepted Answer

A)  $x = \frac { 2 } { 5 }$ 
B)  $x = \frac { 1 } { 90 }$ 
C)  $x = \frac { 5 } { 2 }$ 
D)  $x = 90$ 
A)  $x = \frac { 2 } { 5 }$ 
B)  $x = \frac { 1 } { 90 }$ 
C)  $x = \frac { 5 } { 2 }$ 
D)  $x = 90$

Question 8

Evaluate the rational function, if possible. $$m ( y ) = \frac { 2 y ^ { 2 } + 5 } { y - 7 } ; m ( 7 )$$

Accepted Answer

A)  $m ( 7 ) = 0$ 
B)  $m ( 7 ) = 103$ 
C)  $m ( 7 ) = 1$ 
D)  $m ( 7 )$ is undefined 
A)  $m ( 7 ) = 0$ 
B)  $m ( 7 ) = 103$ 
C)  $m ( 7 ) = 1$ 
D)  $m ( 7 )$ is undefined

Question 9

Subtract. $\frac { 5 } { 4 t } - \frac { t + 4 } { 10 t ^ { 2 } }$

Accepted Answer

A)  $\frac { 23 t - 8 } { 20 t ^ { 2 } }$ 
B)  $\frac { 50 - 4 t - t ^ { 2 } } { 40 t ^ { 3 } }$ 
C)  $\frac { 23 t + 8 } { 20 t ^ { 2 } }$ 
D)  $\frac { 1 - t } { 4 t - 10 t ^ { 2 } }$ 
A)  $\frac { 23 t - 8 } { 20 t ^ { 2 } }$ 
B)  $\frac { 50 - 4 t - t ^ { 2 } } { 40 t ^ { 3 } }$ 
C)  $\frac { 23 t + 8 } { 20 t ^ { 2 } }$ 
D)  $\frac { 1 - t } { 4 t - 10 t ^ { 2 } }$

Question 10

A kayaker can row 6 miles upstream, against a 2 mph current, in one hour more than he can row 7 miles downstream. What is his average speed in still water?

Accepted Answer

A)  3 mph 
B)  5 mph 
C)  6.5 mph 
D)  8 mph 
A)  3 mph 
B)  5 mph 
C)  6.5 mph 
D)  8 mph

Question 11

In the equation $p = \frac { 1 } { q }$ , does p vary directly or inversely with q?

Accepted Answer

A)  Directly 
B)  Inversely 
A)  Directly 
B)  Inversely

Question 12

Nancy shot a 12 on 3 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes? Round to nearest whole number.

Accepted Answer

A)  84 strokes 
B)  72 strokes 
C)  66 strokes 
D)  60 strokes 
A)  84 strokes 
B)  72 strokes 
C)  66 strokes 
D)  60 strokes

Question 13

A postal worker can sort a day's worth of mail in 8 hours. With her supervisor helping, it takes 3 hours. How long would it take the supervisor working alone?

Accepted Answer

A)  4 hrs. 48 min. 
B)  5 hrs. 20 min. 
C)  2 hrs. 11 min. 
D)  3 hrs. 50 min. 
A)  4 hrs. 48 min. 
B)  5 hrs. 20 min. 
C)  2 hrs. 11 min. 
D)  3 hrs. 50 min.

Question 14

$R$ varies directly as $x ^ { 2 }$ and inversely as $t$ when $R = 14$ when $x = 7$ and $t = 21$. Find $R$ when $x = 4$ and $t = 9$.

Accepted Answer

The answer of $R$ varies directly as \(x ^ {...

Question 15

Simplify the rational expression. $$\frac { y ^ { 2 } + 2 y - 63 } { y ^ { 2 } - 49 }$$

Accepted Answer

A)  $\frac { y + 9 } { y + 7 } \quad$ (Provided $y \neq 7$ ) 
B)  $\frac { 2 y - 63 } { 49 } \quad$ (Provided $\left. y \neq - 7 \right)$ 
C)  $\frac { y + 9 } { y - 7 } \quad$ (Provided $\left. y \neq - 7 \right)$ 
D)  $\frac { y ^ { 2 } + 2 y - 63 } { y ^ { 2 } - 49 }$; cannot be simplified 
A)  $\frac { y + 9 } { y + 7 } \quad$ (Provided $y \neq 7$ ) 
B)  $\frac { 2 y - 63 } { 49 } \quad$ (Provided $\left. y \neq - 7 \right)$ 
C)  $\frac { y + 9 } { y - 7 } \quad$ (Provided $\left. y \neq - 7 \right)$ 
D)  $\frac { y ^ { 2 } + 2 y - 63 } { y ^ { 2 } - 49 }$; cannot be simplified

Question 16

Divide the rational expressions. $$\frac { 3 x ^ { 2 } + 3 x } { 2 } \div \frac { x ^ { 2 } - 1 } { 6 x }$$

Accepted Answer

A)  $\frac { ( x + 1 ) \left( x ^ { 2 } - 1 \right) } { 4 }$ 
B)  $\frac { x - 1 } { 9 x ^ { 2 } }$ 
C)  $\frac { x ( x + 1 ) ( x - 1 ) } { 4 }$ 
D)  $\frac { 9 x ^ { 2 } } { x - 1 }$ 
A)  $\frac { ( x + 1 ) \left( x ^ { 2 } - 1 \right) } { 4 }$ 
B)  $\frac { x - 1 } { 9 x ^ { 2 } }$ 
C)  $\frac { x ( x + 1 ) ( x - 1 ) } { 4 }$ 
D)  $\frac { 9 x ^ { 2 } } { x - 1 }$

Question 17

If 9 is decreased by the reciprocal of a number, the result is $\frac { 7 } { 3 }$. Find the number.

Accepted Answer

A)  $\frac { 20 } { 3 }$ 
B)  $\frac { 34 } { 3 }$ 
C)  $\frac { 3 } { 34 }$ 
D)  $\frac { 3 } { 20 }$ 
A)  $\frac { 20 } { 3 }$ 
B)  $\frac { 34 } { 3 }$ 
C)  $\frac { 3 } { 34 }$ 
D)  $\frac { 3 } { 20 }$

Question 18

Fill in the blank to make an equivalent fraction with the given denominator. $$\frac { 8 } { 5 t } = \frac { } { 15 t ^ { 2 } z }$$

Accepted Answer

A)  $t z$ 
B)  $3 t z$ 
C)  $24 t z$ 
D)  $120 t ^ { 2 } z$ 
A)  $t z$ 
B)  $3 t z$ 
C)  $24 t z$ 
D)  $120 t ^ { 2 } z$

Question 19

a. Factor the numerator and denominator.
b. Write the restrictions on y.
c. Simplify the expression. $$\frac { y ^ { 3 } - 5 y ^ { 2 } - 14 y } { 5 y ^ { 2 } + 10 y }$$

Accepted Answer

The answer of a. Factor the numerator and denominator.
b. Write...

Question 20

Subtract. $$\frac { 2 y } { 4 y ^ { 2 } + y } - \frac { 3 + y } { 4 y ^ { 2 } - 23 y - 6 }$$

Accepted Answer

A)  $\frac { y - 15 } { ( 4 y + 1 ) ( y - 6 ) }$ 
B)  $\frac { 3 y ^ { 2 } - 12 y - 3 } { y ( 4 y + 1 ) ( y - 6 ) }$ 
C)  $\frac { y - 3 } { 24 y + 6 }$ 
D)  $\frac { 3 ( y - 5 ) } { ( 4 y + 1 ) ( y - 6 ) }$ 
A)  $\frac { y - 15 } { ( 4 y + 1 ) ( y - 6 ) }$ 
B)  $\frac { 3 y ^ { 2 } - 12 y - 3 } { y ( 4 y + 1 ) ( y - 6 ) }$ 
C)  $\frac { y - 3 } { 24 y + 6 }$ 
D)  $\frac { 3 ( y - 5 ) } { ( 4 y + 1 ) ( y - 6 ) }$

Simplify the complex fraction by using Method II. $\frac { \frac { 56 x ^ { 2 } + 32 x } { x - 8 } } { \frac { 4 + 7 x } { 24 - 3 x } }$

Write the domain of the rational function in interval notation. $k ( x ) = \frac { x ( x + 7 ) } { x ( x - 12 ) ( x + 7 ) }$

Simplify the complex fraction by using Method II. $\frac { \frac { 2 x + 3 } { x ^ { 3 } } } { 5 x - \frac { x ^ { 2 } + 9 } { x } }$

Solve for b. $h = \frac { 2 A } { B + b }$

Add or subtract as indicated and simplify if possible. $\frac { 13 x } { - 3 x + 4 } + \frac { 7 } { - 3 x + 4 }$

Find the least common denominator (LCD). $\frac { 10 x } { x + 10 } , \frac { 17 } { x ^ { 2 } - 100 }$

x varies directly as p. If x = 48 when p = 8, find x when p is 15.

Evaluate the rational function, if possible. $m ( y ) = \frac { 2 y ^ { 2 } + 5 } { y - 7 } ; m ( 7 )$

Subtract. $\frac { 5 } { 4 t } - \frac { t + 4 } { 10 t ^ { 2 } }$

A kayaker can row 6 miles upstream, against a 2 mph current, in one hour more than he can row 7 miles downstream. What is his average speed in still water?

In the equation $p = \frac { 1 } { q }$ , does p vary directly or inversely with q?

Nancy shot a 12 on 3 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes? Round to nearest whole number.

A postal worker can sort a day's worth of mail in 8 hours. With her supervisor helping, it takes 3 hours. How long would it take the supervisor working alone?

$R$ varies directly as $x ^ { 2 }$ and inversely as $t$ when $R = 14$ when $x = 7$ and $t = 21$ . Find $R$ when $x = 4$ and $t = 9$ .

Simplify the rational expression. $\frac { y ^ { 2 } + 2 y - 63 } { y ^ { 2 } - 49 }$

Divide the rational expressions. $\frac { 3 x ^ { 2 } + 3 x } { 2 } \div \frac { x ^ { 2 } - 1 } { 6 x }$

If 9 is decreased by the reciprocal of a number, the result is $\frac { 7 } { 3 }$ . Find the number.

Fill in the blank to make an equivalent fraction with the given denominator. $\frac { 8 } { 5 t } = \frac { } { 15 t ^ { 2 } z }$

a. Factor the numerator and denominator. b. Write the restrictions on y. c. Simplify the expression. $\frac { y ^ { 3 } - 5 y ^ { 2 } - 14 y } { 5 y ^ { 2 } + 10 y }$

Subtract. $\frac { 2 y } { 4 y ^ { 2 } + y } - \frac { 3 + y } { 4 y ^ { 2 } - 23 y - 6 }$

Linear Equations and Inequalities in One Variable

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Exam 5: Rational Expressions and Rational Equations

Simplify the complex fraction by using Method II. 56x2+32xx−84+7x24−3x\frac { \frac { 56 x ^ { 2 } + 32 x } { x - 8 } } { \frac { 4 + 7 x } { 24 - 3 x } }24−3x4+7x​x−856x2+32x​​

Write the domain of the rational function in interval notation. k(x)=x(x+7)x(x−12)(x+7)k ( x ) = \frac { x ( x + 7 ) } { x ( x - 12 ) ( x + 7 ) }k(x)=x(x−12)(x+7)x(x+7)​

Simplify the complex fraction by using Method II. 2x+3x35x−x2+9x\frac { \frac { 2 x + 3 } { x ^ { 3 } } } { 5 x - \frac { x ^ { 2 } + 9 } { x } }5x−xx2+9​x32x+3​​

Solve for b. h=2AB+bh = \frac { 2 A } { B + b }h=B+b2A​

Add or subtract as indicated and simplify if possible. 13x−3x+4+7−3x+4\frac { 13 x } { - 3 x + 4 } + \frac { 7 } { - 3 x + 4 }−3x+413x​+−3x+47​

Find the least common denominator (LCD). 10xx+10,17x2−100\frac { 10 x } { x + 10 } , \frac { 17 } { x ^ { 2 } - 100 }x+1010x​,x2−10017​

x varies directly as p. If x = 48 when p = 8, find x when p is 15.

Evaluate the rational function, if possible. m(y)=2y2+5y−7;m(7)m ( y ) = \frac { 2 y ^ { 2 } + 5 } { y - 7 } ; m ( 7 )m(y)=y−72y2+5​;m(7)

Subtract. 54t−t+410t2\frac { 5 } { 4 t } - \frac { t + 4 } { 10 t ^ { 2 } }4t5​−10t2t+4​

A kayaker can row 6 miles upstream, against a 2 mph current, in one hour more than he can row 7 miles downstream. What is his average speed in still water?

In the equation p=1qp = \frac { 1 } { q }p=q1​ , does p vary directly or inversely with q?

Nancy shot a 12 on 3 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes? Round to nearest whole number.

A postal worker can sort a day's worth of mail in 8 hours. With her supervisor helping, it takes 3 hours. How long would it take the supervisor working alone?

RRR varies directly as x2x ^ { 2 }x2 and inversely as ttt when R=14R = 14R=14 when x=7x = 7x=7 and t=21t = 21t=21 . Find RRR when x=4x = 4x=4 and t=9t = 9t=9 .

Simplify the rational expression. y2+2y−63y2−49\frac { y ^ { 2 } + 2 y - 63 } { y ^ { 2 } - 49 }y2−49y2+2y−63​

Divide the rational expressions. 3x2+3x2÷x2−16x\frac { 3 x ^ { 2 } + 3 x } { 2 } \div \frac { x ^ { 2 } - 1 } { 6 x }23x2+3x​÷6xx2−1​

If 9 is decreased by the reciprocal of a number, the result is 73\frac { 7 } { 3 }37​ . Find the number.

Fill in the blank to make an equivalent fraction with the given denominator. 85t=15t2z\frac { 8 } { 5 t } = \frac { } { 15 t ^ { 2 } z }5t8​=15t2z​

a. Factor the numerator and denominator. b. Write the restrictions on y. c. Simplify the expression. y3−5y2−14y5y2+10y\frac { y ^ { 3 } - 5 y ^ { 2 } - 14 y } { 5 y ^ { 2 } + 10 y }5y2+10yy3−5y2−14y​

Subtract. 2y4y2+y−3+y4y2−23y−6\frac { 2 y } { 4 y ^ { 2 } + y } - \frac { 3 + y } { 4 y ^ { 2 } - 23 y - 6 }4y2+y2y​−4y2−23y−63+y​

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

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Simplify the complex fraction by using Method II. $\frac { \frac { 56 x ^ { 2 } + 32 x } { x - 8 } } { \frac { 4 + 7 x } { 24 - 3 x } }$

Write the domain of the rational function in interval notation. $k ( x ) = \frac { x ( x + 7 ) } { x ( x - 12 ) ( x + 7 ) }$

Simplify the complex fraction by using Method II. $\frac { \frac { 2 x + 3 } { x ^ { 3 } } } { 5 x - \frac { x ^ { 2 } + 9 } { x } }$

Solve for b. $h = \frac { 2 A } { B + b }$

Add or subtract as indicated and simplify if possible. $\frac { 13 x } { - 3 x + 4 } + \frac { 7 } { - 3 x + 4 }$

Find the least common denominator (LCD). $\frac { 10 x } { x + 10 } , \frac { 17 } { x ^ { 2 } - 100 }$

Evaluate the rational function, if possible. $m ( y ) = \frac { 2 y ^ { 2 } + 5 } { y - 7 } ; m ( 7 )$

Subtract. $\frac { 5 } { 4 t } - \frac { t + 4 } { 10 t ^ { 2 } }$

In the equation $p = \frac { 1 } { q }$ , does p vary directly or inversely with q?

$R$ varies directly as $x ^ { 2 }$ and inversely as $t$ when $R = 14$ when $x = 7$ and $t = 21$ . Find $R$ when $x = 4$ and $t = 9$ .

Simplify the rational expression. $\frac { y ^ { 2 } + 2 y - 63 } { y ^ { 2 } - 49 }$

Divide the rational expressions. $\frac { 3 x ^ { 2 } + 3 x } { 2 } \div \frac { x ^ { 2 } - 1 } { 6 x }$

If 9 is decreased by the reciprocal of a number, the result is $\frac { 7 } { 3 }$ . Find the number.

Fill in the blank to make an equivalent fraction with the given denominator. $\frac { 8 } { 5 t } = \frac { } { 15 t ^ { 2 } z }$

a. Factor the numerator and denominator. b. Write the restrictions on y. c. Simplify the expression. $\frac { y ^ { 3 } - 5 y ^ { 2 } - 14 y } { 5 y ^ { 2 } + 10 y }$

Subtract. $\frac { 2 y } { 4 y ^ { 2 } + y } - \frac { 3 + y } { 4 y ^ { 2 } - 23 y - 6 }$