Question 1

Multiply the rational expressions. $$\frac { 2 x ^ { 2 } - 4 x - 6 } { x + 2 } \cdot \frac { x ^ { 2 } - 4 } { 2 x ^ { 2 } + 2 x }$$

Accepted Answer

A)  $\frac { ( x - 3 ) ( x - 2 ) ^ { 2 } } { x ( x + 2 ) }$ 
B)  $\frac { ( x - 3 ) ( x - 2 ) } { x }$ 
C)  $\frac { ( 2 x + 2 ) ( x - 3 ) } { x + 2 }$ 
D)  $\frac { ( x - 3 ) ( x + 2 ) } { 2 x ^ { 2 } + 2 x }$ 
A)  $\frac { ( x - 3 ) ( x - 2 ) ^ { 2 } } { x ( x + 2 ) }$ 
B)  $\frac { ( x - 3 ) ( x - 2 ) } { x }$ 
C)  $\frac { ( 2 x + 2 ) ( x - 3 ) } { x + 2 }$ 
D)  $\frac { ( x - 3 ) ( x + 2 ) } { 2 x ^ { 2 } + 2 x }$ B

Question 2

Divide the rational expressions. $$\frac { 2 y ^ { 7 } } { x ^ { 9 } } \div \frac { 8 y ^ { 2 } } { 3 x }$$

Accepted Answer

A)  $\frac { 3 x ^ { 10 } } { 16 y ^ { 9 } }$ 
B)  $\frac { 16 y ^ { 9 } } { 3 x ^ { 10 } }$ 
C)  $\frac { 3 y ^ { 5 } } { 4 x ^ { 8 } }$ 
D)  $\frac { 4 x ^ { 8 } } { 3 y ^ { 5 } }$ 
A)  $\frac { 3 x ^ { 10 } } { 16 y ^ { 9 } }$ 
B)  $\frac { 16 y ^ { 9 } } { 3 x ^ { 10 } }$ 
C)  $\frac { 3 y ^ { 5 } } { 4 x ^ { 8 } }$ 
D)  $\frac { 4 x ^ { 8 } } { 3 y ^ { 5 } }$ C

Question 3

Solve the rational equation. $$\frac { 1 } { x } + \frac { 5 } { 2 } = \frac { 7 } { 4 }$$

Accepted Answer

$$\left\{ - \frac { 4 } { 3 } \right\}$$

Question 4

Multiply the rational expressions. $$\frac { 5 - 7 y } { y } \cdot \frac { y ^ { 2 } } { 7 y ^ { 2 } + 2 y - 5 }$$

Accepted Answer

The answer of Multiply the rational expressions. \[\frac { 5...

Question 5

Solve the rational equation. $$\frac { t ^ { 2 } } { 3 } - \frac { t } { 6 } = 1$$

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\left\{ - \frac { 3 } { 2 } , 2 \right\}$ 
C)  $\left\{ - 2 , \frac { 3 } { 2 } \right\}$ 
D)  \{ \} 
A)  $\{ 2 \}$ 
B)  $\left\{ - \frac { 3 } { 2 } , 2 \right\}$ 
C)  $\left\{ - 2 , \frac { 3 } { 2 } \right\}$ 
D)  \{ \}

Question 6

Write a variation model. Use k as the constant of variation. Y varies inversely as the square root of z.

Accepted Answer

A)  $Y = k \sqrt { z }$ 
B)  $Y = \frac { k } { z ^ { 2 } }$ 
C)  $Y = \frac { k } { \sqrt { z } }$ 
D)  $Y = k z ^ { 2 }$ 
A)  $Y = k \sqrt { z }$ 
B)  $Y = \frac { k } { z ^ { 2 } }$ 
C)  $Y = \frac { k } { \sqrt { z } }$ 
D)  $Y = k z ^ { 2 }$

Question 7

Simplify the rational expression. $$\frac { 12 y ^ { 2 } - 3 y ^ { 3 } } { y ^ { 2 } - 3 y - 4 }$$

Accepted Answer

A)  $\frac { 12 - 3 y ^ { 3 } } { - 3 y - 4 }$ (Provided $\left. y \neq 4 \right)$ 
B)  $\frac { 3 y ^ { 2 } } { y + 1 } ($ Provided $y \neq 4 )$ 
C)  $- \frac { 3 y ^ { 2 } } { y + 1 } ($ Provided $y \neq 4 )$ 
D)  $\frac { 12 y ^ { 2 } - 3 y ^ { 3 } } { y ^ { 2 } - 3 y - 4 }$; cannot be simplified 
A)  $\frac { 12 - 3 y ^ { 3 } } { - 3 y - 4 }$ (Provided $\left. y \neq 4 \right)$ 
B)  $\frac { 3 y ^ { 2 } } { y + 1 } ($ Provided $y \neq 4 )$ 
C)  $- \frac { 3 y ^ { 2 } } { y + 1 } ($ Provided $y \neq 4 )$ 
D)  $\frac { 12 y ^ { 2 } - 3 y ^ { 3 } } { y ^ { 2 } - 3 y - 4 }$; cannot be simplified

Question 8

Solve for r. $$I = \frac { E } { R + r }$$

Accepted Answer

A)  $r = E - R$ 
B)  $r = \frac { I E - R } { I }$ 
C)  $r = \frac { E - I R } { I }$ 
D)  $r = \frac { R - I E } { I }$ 
A)  $r = E - R$ 
B)  $r = \frac { I E - R } { I }$ 
C)  $r = \frac { E - I R } { I }$ 
D)  $r = \frac { R - I E } { I }$

Question 9

Solve the proportion. $$\frac { 5 } { y - 2 } = \frac { 15 } { 2 }$$

Accepted Answer

The answer of Solve the proportion. \[\frac { 5 }...

Question 10

Subtract. $$\frac { x } { x + 3 } - \frac { 3 - x ^ { 2 } } { x ^ { 2 } - 9 }$$

Accepted Answer

A)  $\frac { x ^ { 3 } + 3 x - 3 } { \left( x ^ { 2 } - 9 \right) ( x + 3 ) }$ 
B)  $\frac { - 3 x - 3 } { x ^ { 2 } - 9 }$ 
C)  $\frac { 2 x ^ { 2 } - 3 x - 3 } { x ^ { 2 } - 9 }$ 
D)  $\frac { x ^ { 2 } + x - 3 } { - x ^ { 2 } + x + 12 }$ 
A)  $\frac { x ^ { 3 } + 3 x - 3 } { \left( x ^ { 2 } - 9 \right) ( x + 3 ) }$ 
B)  $\frac { - 3 x - 3 } { x ^ { 2 } - 9 }$ 
C)  $\frac { 2 x ^ { 2 } - 3 x - 3 } { x ^ { 2 } - 9 }$ 
D)  $\frac { x ^ { 2 } + x - 3 } { - x ^ { 2 } + x + 12 }$

Question 11

Simplify. $$\frac { 3 } { 2 y } + \frac { y - 5 } { 3 y ^ { 2 } } - \frac { 5 } { 4 y }$$

Accepted Answer

A)  $\frac { y - 7 } { 3 y ^ { 2 } - 2 y }$ 
B)  $\frac { 37 y - 20 } { 12 y ^ { 2 } }$ 
C)  $\frac { y ^ { 3 } + 3 y ^ { 2 } - 5 } { 24 y ^ { 4 } }$ 
D)  $\frac { 7 y - 20 } { 12 y ^ { 2 } }$ 
A)  $\frac { y - 7 } { 3 y ^ { 2 } - 2 y }$ 
B)  $\frac { 37 y - 20 } { 12 y ^ { 2 } }$ 
C)  $\frac { y ^ { 3 } + 3 y ^ { 2 } - 5 } { 24 y ^ { 4 } }$ 
D)  $\frac { 7 y - 20 } { 12 y ^ { 2 } }$

Question 12

The two triangles pictured below are similar triangles. If side a is 6", side b is 4", and side c is 7.5", find the length of side d.

Accepted Answer

A)  $5.6 ^ { \prime \prime }$ 
B)  $5 ^ { \prime \prime }$ 
C)  $3.2 ^ { \prime \prime }$ 
D)  $5.5 ^ { \prime \prime }$ 
A)  $5.6 ^ { \prime \prime }$ 
B)  $5 ^ { \prime \prime }$ 
C)  $3.2 ^ { \prime \prime }$ 
D)  $5.5 ^ { \prime \prime }$

Question 13

Add or subtract as indicated and simplify if possible. $$\frac { 19 y } { 11 x } + \frac { 39 y } { 11 x }$$

Accepted Answer

A)  $\frac { 741 y ^ { 2 } } { 121 x ^ { 2 } }$ 
B)  $\frac { 58 y } { 11 x }$ 
C)  $\frac { 58 y } { 22 x }$ 
D)  $\frac { 58 y } { 44 x }$ 
A)  $\frac { 741 y ^ { 2 } } { 121 x ^ { 2 } }$ 
B)  $\frac { 58 y } { 11 x }$ 
C)  $\frac { 58 y } { 22 x }$ 
D)  $\frac { 58 y } { 44 x }$

Question 14

Simplify the rational expression. $$\frac { 18 a ^ { 5 } b ^ { 7 } } { 6 a ^ { 2 } b ^ { 2 } }$$

Accepted Answer

The answer of Simplify the rational expression. \[\frac { 18...

Question 15

Solve the rational equation. $$\frac { 1 } { 3 y } - \frac { y - 1 } { 2 y } - \frac { 1 } { 3 } = - \frac { y + 3 } { 6 y }$$

Accepted Answer

The answer of Solve the rational equation. \[\frac { 1...

Question 16

Solve the rational equation. $$\frac { 6 } { x - 3 } - \frac { 18 } { x ( x - 3 ) } = - 2$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 3 } , \frac { 1 } { 3 } \right\}$ 
B)  $\{ - 3,3 \}$ 
C)  $\{ - 3 \}$ 
D) {  } 
A)  $\left\{ - \frac { 1 } { 3 } , \frac { 1 } { 3 } \right\}$ 
B)  $\{ - 3,3 \}$ 
C)  $\{ - 3 \}$ 
D) {  }

Question 17

Add. $$\frac { - 2 y } { 2 y ^ { 2 } + 5 y } + \frac { y - 3 } { 2 y ^ { 2 } + y - 10 }$$

Accepted Answer

A)  $\frac { - 2 y ^ { 2 } + y - 3 } { 2 y ^ { 3 } + 5 y ^ { 2 } - 10 }$ 
B)  $\frac { 1 - y } { ( 2 y + 5 ) ( y - 2 ) }$ 
C)  $\frac { - y - 3 } { 4 y ^ { 2 } + 6 y - 10 }$ 
D)  $\frac { - 3 y ^ { 2 } + y + 1 } { y ( 2 y + 5 ) ( y - 2 ) }$ 
A)  $\frac { - 2 y ^ { 2 } + y - 3 } { 2 y ^ { 3 } + 5 y ^ { 2 } - 10 }$ 
B)  $\frac { 1 - y } { ( 2 y + 5 ) ( y - 2 ) }$ 
C)  $\frac { - y - 3 } { 4 y ^ { 2 } + 6 y - 10 }$ 
D)  $\frac { - 3 y ^ { 2 } + y + 1 } { y ( 2 y + 5 ) ( y - 2 ) }$

Question 18

Evaluate the rational function, if possible. $$f ( z ) = \frac { 16 + 4 z } { 2 - 3 z } ; f \left( \frac { 1 } { 2 } \right)$$

Accepted Answer

The answer of Evaluate the rational function, if possible. \[f...

Question 19

The amount of medicine that a physician prescribes for a patient varies directly as the weight of the patient. A physician prescribes 3 grams (g) of a medicine for a 75-lb person.
a. How many grams should be prescribed for a 145-lb person?
b. How many grams should be prescribed for a 180-lb person?
c. How many grams should be prescribed for a 120-lb person?

Accepted Answer

a. 5.8 g
b

Question 20

Find the least common denominator (LCD). $$\frac { 5 } { 9 - 24 t } , \frac { 3 t - 2 } { 8 t ^ { 2 } + 5 t - 3 }$$

Accepted Answer

The answer of Find the least common denominator (LCD). \[\frac...

Multiply the rational expressions. $\frac { 2 x ^ { 2 } - 4 x - 6 } { x + 2 } \cdot \frac { x ^ { 2 } - 4 } { 2 x ^ { 2 } + 2 x }$

Divide the rational expressions. $\frac { 2 y ^ { 7 } } { x ^ { 9 } } \div \frac { 8 y ^ { 2 } } { 3 x }$

Solve the rational equation. $\frac { 1 } { x } + \frac { 5 } { 2 } = \frac { 7 } { 4 }$

Multiply the rational expressions. $\frac { 5 - 7 y } { y } \cdot \frac { y ^ { 2 } } { 7 y ^ { 2 } + 2 y - 5 }$

Solve the rational equation. $\frac { t ^ { 2 } } { 3 } - \frac { t } { 6 } = 1$

Write a variation model. Use k as the constant of variation. Y varies inversely as the square root of z.

Simplify the rational expression. $\frac { 12 y ^ { 2 } - 3 y ^ { 3 } } { y ^ { 2 } - 3 y - 4 }$

Solve for r. $I = \frac { E } { R + r }$

Solve the proportion. $\frac { 5 } { y - 2 } = \frac { 15 } { 2 }$

Subtract. $\frac { x } { x + 3 } - \frac { 3 - x ^ { 2 } } { x ^ { 2 } - 9 }$

Simplify. $\frac { 3 } { 2 y } + \frac { y - 5 } { 3 y ^ { 2 } } - \frac { 5 } { 4 y }$

The two triangles pictured below are similar triangles. If side a is 6", side b is 4", and side c is 7.5", find the length of side d.

Add or subtract as indicated and simplify if possible. $\frac { 19 y } { 11 x } + \frac { 39 y } { 11 x }$

Simplify the rational expression. $\frac { 18 a ^ { 5 } b ^ { 7 } } { 6 a ^ { 2 } b ^ { 2 } }$

Solve the rational equation. $\frac { 1 } { 3 y } - \frac { y - 1 } { 2 y } - \frac { 1 } { 3 } = - \frac { y + 3 } { 6 y }$

Solve the rational equation. $\frac { 6 } { x - 3 } - \frac { 18 } { x ( x - 3 ) } = - 2$

Add. $\frac { - 2 y } { 2 y ^ { 2 } + 5 y } + \frac { y - 3 } { 2 y ^ { 2 } + y - 10 }$

Evaluate the rational function, if possible. $f ( z ) = \frac { 16 + 4 z } { 2 - 3 z } ; f \left( \frac { 1 } { 2 } \right)$

Find the least common denominator (LCD). $\frac { 5 } { 9 - 24 t } , \frac { 3 t - 2 } { 8 t ^ { 2 } + 5 t - 3 }$

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

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Exam 5: Rational Expressions and Rational Equations

Multiply the rational expressions. 2x2−4x−6x+2⋅x2−42x2+2x\frac { 2 x ^ { 2 } - 4 x - 6 } { x + 2 } \cdot \frac { x ^ { 2 } - 4 } { 2 x ^ { 2 } + 2 x }x+22x2−4x−6​⋅2x2+2xx2−4​

Divide the rational expressions. 2y7x9÷8y23x\frac { 2 y ^ { 7 } } { x ^ { 9 } } \div \frac { 8 y ^ { 2 } } { 3 x }x92y7​÷3x8y2​

Solve the rational equation. 1x+52=74\frac { 1 } { x } + \frac { 5 } { 2 } = \frac { 7 } { 4 }x1​+25​=47​

Multiply the rational expressions. 5−7yy⋅y27y2+2y−5\frac { 5 - 7 y } { y } \cdot \frac { y ^ { 2 } } { 7 y ^ { 2 } + 2 y - 5 }y5−7y​⋅7y2+2y−5y2​

Solve the rational equation. t23−t6=1\frac { t ^ { 2 } } { 3 } - \frac { t } { 6 } = 13t2​−6t​=1

Write a variation model. Use k as the constant of variation. Y varies inversely as the square root of z.

Simplify the rational expression. 12y2−3y3y2−3y−4\frac { 12 y ^ { 2 } - 3 y ^ { 3 } } { y ^ { 2 } - 3 y - 4 }y2−3y−412y2−3y3​

Solve for r. I=ER+rI = \frac { E } { R + r }I=R+rE​

Solve the proportion. 5y−2=152\frac { 5 } { y - 2 } = \frac { 15 } { 2 }y−25​=215​

Subtract. xx+3−3−x2x2−9\frac { x } { x + 3 } - \frac { 3 - x ^ { 2 } } { x ^ { 2 } - 9 }x+3x​−x2−93−x2​

Simplify. 32y+y−53y2−54y\frac { 3 } { 2 y } + \frac { y - 5 } { 3 y ^ { 2 } } - \frac { 5 } { 4 y }2y3​+3y2y−5​−4y5​

The two triangles pictured below are similar triangles. If side a is 6", side b is 4", and side c is 7.5", find the length of side d.

Add or subtract as indicated and simplify if possible. 19y11x+39y11x\frac { 19 y } { 11 x } + \frac { 39 y } { 11 x }11x19y​+11x39y​

Simplify the rational expression. 18a5b76a2b2\frac { 18 a ^ { 5 } b ^ { 7 } } { 6 a ^ { 2 } b ^ { 2 } }6a2b218a5b7​

Solve the rational equation. 13y−y−12y−13=−y+36y\frac { 1 } { 3 y } - \frac { y - 1 } { 2 y } - \frac { 1 } { 3 } = - \frac { y + 3 } { 6 y }3y1​−2yy−1​−31​=−6yy+3​

Solve the rational equation. 6x−3−18x(x−3)=−2\frac { 6 } { x - 3 } - \frac { 18 } { x ( x - 3 ) } = - 2x−36​−x(x−3)18​=−2

Add. −2y2y2+5y+y−32y2+y−10\frac { - 2 y } { 2 y ^ { 2 } + 5 y } + \frac { y - 3 } { 2 y ^ { 2 } + y - 10 }2y2+5y−2y​+2y2+y−10y−3​

Evaluate the rational function, if possible. f(z)=16+4z2−3z;f(12)f ( z ) = \frac { 16 + 4 z } { 2 - 3 z } ; f \left( \frac { 1 } { 2 } \right)f(z)=2−3z16+4z​;f(21​)

Find the least common denominator (LCD). 59−24t,3t−28t2+5t−3\frac { 5 } { 9 - 24 t } , \frac { 3 t - 2 } { 8 t ^ { 2 } + 5 t - 3 }9−24t5​,8t2+5t−33t−2​

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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Multiply the rational expressions. $\frac { 2 x ^ { 2 } - 4 x - 6 } { x + 2 } \cdot \frac { x ^ { 2 } - 4 } { 2 x ^ { 2 } + 2 x }$

Divide the rational expressions. $\frac { 2 y ^ { 7 } } { x ^ { 9 } } \div \frac { 8 y ^ { 2 } } { 3 x }$

Solve the rational equation. $\frac { 1 } { x } + \frac { 5 } { 2 } = \frac { 7 } { 4 }$

Multiply the rational expressions. $\frac { 5 - 7 y } { y } \cdot \frac { y ^ { 2 } } { 7 y ^ { 2 } + 2 y - 5 }$

Solve the rational equation. $\frac { t ^ { 2 } } { 3 } - \frac { t } { 6 } = 1$

Simplify the rational expression. $\frac { 12 y ^ { 2 } - 3 y ^ { 3 } } { y ^ { 2 } - 3 y - 4 }$

Solve for r. $I = \frac { E } { R + r }$

Solve the proportion. $\frac { 5 } { y - 2 } = \frac { 15 } { 2 }$

Subtract. $\frac { x } { x + 3 } - \frac { 3 - x ^ { 2 } } { x ^ { 2 } - 9 }$

Simplify. $\frac { 3 } { 2 y } + \frac { y - 5 } { 3 y ^ { 2 } } - \frac { 5 } { 4 y }$

Add or subtract as indicated and simplify if possible. $\frac { 19 y } { 11 x } + \frac { 39 y } { 11 x }$

Simplify the rational expression. $\frac { 18 a ^ { 5 } b ^ { 7 } } { 6 a ^ { 2 } b ^ { 2 } }$

Solve the rational equation. $\frac { 1 } { 3 y } - \frac { y - 1 } { 2 y } - \frac { 1 } { 3 } = - \frac { y + 3 } { 6 y }$

Solve the rational equation. $\frac { 6 } { x - 3 } - \frac { 18 } { x ( x - 3 ) } = - 2$

Add. $\frac { - 2 y } { 2 y ^ { 2 } + 5 y } + \frac { y - 3 } { 2 y ^ { 2 } + y - 10 }$

Evaluate the rational function, if possible. $f ( z ) = \frac { 16 + 4 z } { 2 - 3 z } ; f \left( \frac { 1 } { 2 } \right)$

Find the least common denominator (LCD). $\frac { 5 } { 9 - 24 t } , \frac { 3 t - 2 } { 8 t ^ { 2 } + 5 t - 3 }$