Question 1

Subtract. Simplify, if possible.
-$$\frac { 4 x + 3 y } { 5 x ^ { 2 } y } - \frac { 2 x - 6 y } { x y ^ { 2 } }$$

Accepted Answer

A)  $\frac { 10 x ^ { 2 } - 26 x y + 3 y ^ { 2 } } { 5 x ^ { 2 } y ^ { 2 } }$ 
B)  $\frac { 4 x ^ { 2 } y ^ { 2 } + 3 x y ^ { 3 } - 10 x ^ { 3 } y + 30 x ^ { 2 } y ^ { 2 } } { 5 x ^ { 3 } y ^ { 3 } }$ 
C)  $\frac { 2 x + 9 y } { 5 x ^ { 2 } y ^ { 2 } }$ 
D)  $\frac { - 10 x ^ { 2 } + 34 x y + 3 y ^ { 2 } } { 5 x ^ { 2 } y ^ { 2 } }$ 
A)  $\frac { 10 x ^ { 2 } - 26 x y + 3 y ^ { 2 } } { 5 x ^ { 2 } y ^ { 2 } }$ 
B)  $\frac { 4 x ^ { 2 } y ^ { 2 } + 3 x y ^ { 3 } - 10 x ^ { 3 } y + 30 x ^ { 2 } y ^ { 2 } } { 5 x ^ { 3 } y ^ { 3 } }$ 
C)  $\frac { 2 x + 9 y } { 5 x ^ { 2 } y ^ { 2 } }$ 
D)  $\frac { - 10 x ^ { 2 } + 34 x y + 3 y ^ { 2 } } { 5 x ^ { 2 } y ^ { 2 } }$

Question 2

Add. Simplify, if possible.
-$$\frac { 1 } { m - n ^ { 2 } } + \frac { 3 } { n ^ { 2 } - m }$$

Accepted Answer

A)  $\frac { 3 } { m - n ^ { 2 } }$ 
B)  $\frac { - 2 } { m - n ^ { 2 } }$ 
C)  $\frac { 4 } { m - n ^ { 2 } }$ 
D)  $\frac { 2 } { m - n ^ { 2 } }$ 
A)  $\frac { 3 } { m - n ^ { 2 } }$ 
B)  $\frac { - 2 } { m - n ^ { 2 } }$ 
C)  $\frac { 4 } { m - n ^ { 2 } }$ 
D)  $\frac { 2 } { m - n ^ { 2 } }$

Question 3

Solve the equation.
-$$\frac { 7 } { y + 2 } - \frac { 9 } { y - 2 } = \frac { 4 } { y ^ { 2 } - 4 }$$

Accepted Answer

A)  $\sqrt { 63 }$ 
B)  $- 18$ 
C)  18 
D)  36 
A)  $\sqrt { 63 }$ 
B)  $- 18$ 
C)  18 
D)  36

Question 4

Find an equation of variation in which y varies inversely as x and the following is true.
-$y = 30$, when $x = 2$

Accepted Answer

A)  $y = \frac { 32 } { x }$ 
B)  $y = \frac { 15 } { x }$ 
C)  $y = 15 x$ 
D)  $y = \frac { 60 } { x }$ 
A)  $y = \frac { 32 } { x }$ 
B)  $y = \frac { 15 } { x }$ 
C)  $y = 15 x$ 
D)  $y = \frac { 60 } { x }$

Question 5

Find the LCM.
-$$6 a + 36 , a ^ { 2 } + 6 a$$

Accepted Answer

A)  $6 a ( a + 6 )$ 
B)  $6 a ^ { 2 } + 6$ 
C)  $6 a + 6$ 
D)  $6 a ^ { 2 } + 36$ 
A)  $6 a ( a + 6 )$ 
B)  $6 a ^ { 2 } + 6$ 
C)  $6 a + 6$ 
D)  $6 a ^ { 2 } + 36$

Question 6

Solve the equation.
-$$\frac { x } { x - 2 } - 5 = \frac { 2 } { x - 2 }$$

Accepted Answer

A)  $- 2$ 
B)  $- \frac { 1 } { 2 }$ 
C)  No solution 
D)  2 
A)  $- 2$ 
B)  $- \frac { 1 } { 2 }$ 
C)  No solution 
D)  2

Question 7

Solve.
-The volume $\mathrm { V }$ of a gas varies inversely as the pressure $P$ on it. The volume of a gas is $260 \mathrm {~cm} ^ { 3 }$ under a pressure of $20 \mathrm {~kg} / \mathrm { cm } ^ { 2 }$. What will be its volume under a pressure of $40 \mathrm {~kg} / \mathrm { cm } ^ { 2 }$ ?

Accepted Answer

A)  $130 \mathrm {~cm} ^ { 3 }$ 
B)  $494 \mathrm {~cm} ^ { 3 }$ 
C)  $520 \mathrm {~cm} ^ { 3 }$ 
D)  $137 \mathrm {~cm} ^ { 3 }$ 
A)  $130 \mathrm {~cm} ^ { 3 }$ 
B)  $494 \mathrm {~cm} ^ { 3 }$ 
C)  $520 \mathrm {~cm} ^ { 3 }$ 
D)  $137 \mathrm {~cm} ^ { 3 }$

Question 8

Solve the problem.
-In a cake recipe, the ratio of milk to flour is $\frac { 5 } { 11 }$. If 4 cups of milk are used, how many cups of flour are used?

Accepted Answer

A)  $\frac { 20 } { 11 }$ cups 
B)  $\frac { 55 } { 4 }$ cups 
C)  $\frac { 5 } { 44 }$ cups 
D)  $\frac { 44 } { 5 }$ cups 
A)  $\frac { 20 } { 11 }$ cups 
B)  $\frac { 55 } { 4 }$ cups 
C)  $\frac { 5 } { 44 }$ cups 
D)  $\frac { 44 } { 5 }$ cups

Question 9

Find the reciprocal.
-$$\frac { t + 6 } { t - 4 }$$

Accepted Answer

A)  $\frac { 6 + t } { 4 - t }$ 
B)  $\frac { t - 6 } { t + 4 }$ 
C)  $\frac { t + 4 } { t - 6 }$ 
D)  $\frac { t - 4 } { t + 6 }$ 
A)  $\frac { 6 + t } { 4 - t }$ 
B)  $\frac { t - 6 } { t + 4 }$ 
C)  $\frac { t + 4 } { t - 6 }$ 
D)  $\frac { t - 4 } { t + 6 }$

Question 10

Subtract. Simplify, if possible.
-$$\frac { 3 x - 2 } { 3 x ^ { 3 } } - \frac { 6 x - 7 } { 6 x }$$

Accepted Answer

A)  $\frac { - 6 x ^ { 3 } + 7 x ^ { 2 } + 6 x - 4 } { 6 x ^ { 3 } }$ 
B)  $\frac { - 3 x + 5 } { 6 x ^ { 3 } }$ 
C)  $\frac { - 6 x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 } - 4 x } { 6 x ^ { 4 } }$ 
D)  $\frac { - 3 x ^ { 3 } + 3.5 x ^ { 2 } + 3 x - 2 } { 3 x ^ { 3 } }$ 
A)  $\frac { - 6 x ^ { 3 } + 7 x ^ { 2 } + 6 x - 4 } { 6 x ^ { 3 } }$ 
B)  $\frac { - 3 x + 5 } { 6 x ^ { 3 } }$ 
C)  $\frac { - 6 x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 } - 4 x } { 6 x ^ { 4 } }$ 
D)  $\frac { - 3 x ^ { 3 } + 3.5 x ^ { 2 } + 3 x - 2 } { 3 x ^ { 3 } }$

Question 11

Simplify.
-$$\frac { y ^ { 2 } - 2 y - 35 } { y ^ { 2 } + 2 y - 63 }$$

Accepted Answer

A)  $- \frac { y ^ { 2 } - 2 y - 35 } { y ^ { 2 } + 2 y - 63 }$ 
B)  $\frac { - 2 y - 5 } { 2 y - 9 }$ 
C)  $\frac { y + 5 } { y + 9 }$ 
D)  $\frac { - 2 y - 35 } { 2 y - 63 }$ 
A)  $- \frac { y ^ { 2 } - 2 y - 35 } { y ^ { 2 } + 2 y - 63 }$ 
B)  $\frac { - 2 y - 5 } { 2 y - 9 }$ 
C)  $\frac { y + 5 } { y + 9 }$ 
D)  $\frac { - 2 y - 35 } { 2 y - 63 }$

Question 12

Find the reciprocal.
-$\frac { x } { 8 }$

Accepted Answer

A)  $\frac { 8 } { x }$ 
B)  $- \frac { x } { 8 }$ 
C)  $\frac { 1 } { 8 x }$ 
D)  $1 - \frac { x } { 8 }$ 
A)  $\frac { 8 } { x }$ 
B)  $- \frac { x } { 8 }$ 
C)  $\frac { 1 } { 8 x }$ 
D)  $1 - \frac { x } { 8 }$

Question 13

Find the reciprocal.
-$$9 y ^ { 2 } + 3 y$$

Accepted Answer

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

Question 14

Simplify.
-$\frac { 9 x - 12 } { 9 }$

Accepted Answer

A)  $\frac { 3 x - 4 } { 3 }$ 
B)  $3 x - 4$ 
C)  $\frac { 3 x } { 3 }$ 
D)  $\frac { 3 x - 4 } { 9 }$ 
A)  $\frac { 3 x - 4 } { 3 }$ 
B)  $3 x - 4$ 
C)  $\frac { 3 x } { 3 }$ 
D)  $\frac { 3 x - 4 } { 9 }$

Question 15

Simplify.
-$\frac { \frac { 1 } { 7 } - \frac { 1 } { y } } { \frac { 7 - y } { 7 } }$

Accepted Answer

A)  $\frac { 1 } { y }$ 
B)  $\frac { - 7 } { y }$ 
C)  $\frac { - 1 } { y }$ 
D)  $- \mathrm { y }$ 
A)  $\frac { 1 } { y }$ 
B)  $\frac { - 7 } { y }$ 
C)  $\frac { - 1 } { y }$ 
D)  $- \mathrm { y }$

Question 16

Find the LCM.
-$x ^ { 2 } - 7 x + 10,4 x - 20$

Accepted Answer

A)  $4 ( x + 2 ) ( x + 5 )$ 
B)  $4 ( x - 2 ) ( x + 5 )$ 
C)  $4 ( x + 2 ) ( x - 5 )$ 
D)  $4 ( x - 2 ) ( x - 5 )$ 
A)  $4 ( x + 2 ) ( x + 5 )$ 
B)  $4 ( x - 2 ) ( x + 5 )$ 
C)  $4 ( x + 2 ) ( x - 5 )$ 
D)  $4 ( x - 2 ) ( x - 5 )$

Question 17

Subtract. Simplify, if possible.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 3 } { x ^ { 2 } + 5 x + 4 }$$

Accepted Answer

A)  $\frac { x ^ { 2 } - 2 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
B)  $\frac { x ^ { 2 } - 2 x + 12 } { ( x - 4 ) ( x + 4 ) }$ 
C)  $\frac { x ^ { 2 } - 2 x + 12 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
D)  $\frac { x ^ { 2 } + 2 x + 12 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
A)  $\frac { x ^ { 2 } - 2 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
B)  $\frac { x ^ { 2 } - 2 x + 12 } { ( x - 4 ) ( x + 4 ) }$ 
C)  $\frac { x ^ { 2 } - 2 x + 12 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
D)  $\frac { x ^ { 2 } + 2 x + 12 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

Question 18

Find the equation of variation if the following is true.
-Suppose $p$ varies directly as $\mathrm { q }$ and $\mathrm { p } = 1$ when $\mathrm { q } = \frac { 1 } { 11 }$

Accepted Answer

A)  $p = 12 q$ 
B)  $\mathrm { p } = 11 \mathrm { q }$ 
C)  $\mathrm { p } = \frac { 1 } { 11 } \mathrm { q }$ 
D)  $p = 10 q$ 
A)  $p = 12 q$ 
B)  $\mathrm { p } = 11 \mathrm { q }$ 
C)  $\mathrm { p } = \frac { 1 } { 11 } \mathrm { q }$ 
D)  $p = 10 q$

Question 19

Multiply and, if possible, simplify.
-$$\frac { x ^ { 2 } } { x ^ { 2 } - 4 } \cdot \frac { x ^ { 2 } - 11 x + 18 } { x ^ { 2 } - 9 x }$$

Accepted Answer

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

Question 20

For the pair of similar triangles, find the length of the indicated side.
-In the left triangle, the hypotenuse has length 39 , and the longer leg has length 36 . In the right triangle, the hypotenuse has length 13 , the longer leg has length 12 , and the shorter leg has length 5 . Find the length, $x$, of the shorter leg of the left triangle.

Accepted Answer

A)  $x = 5$ 
B)  $x = 9$ 
C)  $x = 15$ 
D)  $x = 20$ 
A)  $x = 5$ 
B)  $x = 9$ 
C)  $x = 15$ 
D)  $x = 20$

Subtract. Simplify, if possible. - $\frac { 4 x + 3 y } { 5 x ^ { 2 } y } - \frac { 2 x - 6 y } { x y ^ { 2 } }$

Add. Simplify, if possible. - $\frac { 1 } { m - n ^ { 2 } } + \frac { 3 } { n ^ { 2 } - m }$

Solve the equation. - $\frac { 7 } { y + 2 } - \frac { 9 } { y - 2 } = \frac { 4 } { y ^ { 2 } - 4 }$

Find an equation of variation in which y varies inversely as x and the following is true. - $y = 30$ , when $x = 2$

Find the LCM. - $6 a + 36 , a ^ { 2 } + 6 a$

Solve the equation. - $\frac { x } { x - 2 } - 5 = \frac { 2 } { x - 2 }$

Solve. -The volume $\mathrm { V }$ of a gas varies inversely as the pressure $P$ on it. The volume of a gas is $260 \mathrm {~cm} ^ { 3 }$ under a pressure of $20 \mathrm {~kg} / \mathrm { cm } ^ { 2 }$ . What will be its volume under a pressure of $40 \mathrm {~kg} / \mathrm { cm } ^ { 2 }$ ?

Solve the problem. -In a cake recipe, the ratio of milk to flour is $\frac { 5 } { 11 }$ . If 4 cups of milk are used, how many cups of flour are used?

Find the reciprocal. - $\frac { t + 6 } { t - 4 }$

Subtract. Simplify, if possible. - $\frac { 3 x - 2 } { 3 x ^ { 3 } } - \frac { 6 x - 7 } { 6 x }$

Simplify. - $\frac { y ^ { 2 } - 2 y - 35 } { y ^ { 2 } + 2 y - 63 }$

Find the reciprocal. - $\frac { x } { 8 }$

Find the reciprocal. - $9 y ^ { 2 } + 3 y$

Simplify. - $\frac { 9 x - 12 } { 9 }$

Simplify. - $\frac { \frac { 1 } { 7 } - \frac { 1 } { y } } { \frac { 7 - y } { 7 } }$

Find the LCM. - $x ^ { 2 } - 7 x + 10,4 x - 20$

Subtract. Simplify, if possible. - $\frac { x } { x ^ { 2 } - 16 } - \frac { 3 } { x ^ { 2 } + 5 x + 4 }$

Find the equation of variation if the following is true. -Suppose $p$ varies directly as $\mathrm { q }$ and $\mathrm { p } = 1$ when $\mathrm { q } = \frac { 1 } { 11 }$

Multiply and, if possible, simplify. - $\frac { x ^ { 2 } } { x ^ { 2 } - 4 } \cdot \frac { x ^ { 2 } - 11 x + 18 } { x ^ { 2 } - 9 x }$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Filters

Exam 6: Rational Expressions and Equations

Subtract. Simplify, if possible. - 4x+3y5x2y−2x−6yxy2\frac { 4 x + 3 y } { 5 x ^ { 2 } y } - \frac { 2 x - 6 y } { x y ^ { 2 } }5x2y4x+3y​−xy22x−6y​

Add. Simplify, if possible. - 1m−n2+3n2−m\frac { 1 } { m - n ^ { 2 } } + \frac { 3 } { n ^ { 2 } - m }m−n21​+n2−m3​

Solve the equation. - 7y+2−9y−2=4y2−4\frac { 7 } { y + 2 } - \frac { 9 } { y - 2 } = \frac { 4 } { y ^ { 2 } - 4 }y+27​−y−29​=y2−44​

Find an equation of variation in which y varies inversely as x and the following is true. - y=30y = 30y=30 , when x=2x = 2x=2

Find the LCM. - 6a+36,a2+6a6 a + 36 , a ^ { 2 } + 6 a6a+36,a2+6a

Solve the equation. - xx−2−5=2x−2\frac { x } { x - 2 } - 5 = \frac { 2 } { x - 2 }x−2x​−5=x−22​

Solve the problem. -In a cake recipe, the ratio of milk to flour is 511\frac { 5 } { 11 }115​ . If 4 cups of milk are used, how many cups of flour are used?

Find the reciprocal. - t+6t−4\frac { t + 6 } { t - 4 }t−4t+6​

Subtract. Simplify, if possible. - 3x−23x3−6x−76x\frac { 3 x - 2 } { 3 x ^ { 3 } } - \frac { 6 x - 7 } { 6 x }3x33x−2​−6x6x−7​

Simplify. - y2−2y−35y2+2y−63\frac { y ^ { 2 } - 2 y - 35 } { y ^ { 2 } + 2 y - 63 }y2+2y−63y2−2y−35​

Find the reciprocal. - x8\frac { x } { 8 }8x​

Find the reciprocal. - 9y2+3y9 y ^ { 2 } + 3 y9y2+3y

Simplify. - 9x−129\frac { 9 x - 12 } { 9 }99x−12​

Simplify. - 17−1y7−y7\frac { \frac { 1 } { 7 } - \frac { 1 } { y } } { \frac { 7 - y } { 7 } }77−y​71​−y1​​

Find the LCM. - x2−7x+10,4x−20x ^ { 2 } - 7 x + 10,4 x - 20x2−7x+10,4x−20

Subtract. Simplify, if possible. - xx2−16−3x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 3 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+43​

Find the equation of variation if the following is true. -Suppose ppp varies directly as q\mathrm { q }q and p=1\mathrm { p } = 1p=1 when q=111\mathrm { q } = \frac { 1 } { 11 }q=111​

Multiply and, if possible, simplify. - x2x2−4⋅x2−11x+18x2−9x\frac { x ^ { 2 } } { x ^ { 2 } - 4 } \cdot \frac { x ^ { 2 } - 11 x + 18 } { x ^ { 2 } - 9 x }x2−4x2​⋅x2−9xx2−11x+18​