Question 1

Add. Simplify, if possible.
-$$\frac { 6 } { m - n ^ { 2 } } + \frac { 8 } { n ^ { 2 } - m }$$

Accepted Answer

A)  $\frac { - 2 } { m - n ^ { 2 } }$ 
B)  $\frac { 14 } { m - n ^ { 2 } }$ 
C)  $\frac { 48 } { m - n ^ { 2 } }$ 
D)  $\frac { 2 } { m - n ^ { 2 } }$ 
A)  $\frac { - 2 } { m - n ^ { 2 } }$ 
B)  $\frac { 14 } { m - n ^ { 2 } }$ 
C)  $\frac { 48 } { m - n ^ { 2 } }$ 
D)  $\frac { 2 } { m - n ^ { 2 } }$

Question 2

Divide and simplify.
-$$\frac { x ^ { 2 } - 25 } { x } \div \frac { 4 x + 20 } { x - 5 }$$

Accepted Answer

A)  $\frac { 4 x } { ( x - 5 ) ^ { 2 } }$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 4 x }$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { x }$ 
D)  $\frac { 4 ( x + 5 ) ^ { 2 } } { x }$ 
A)  $\frac { 4 x } { ( x - 5 ) ^ { 2 } }$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 4 x }$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { x }$ 
D)  $\frac { 4 ( x + 5 ) ^ { 2 } } { x }$

Question 3

Subtract. Simplify, if possible.
-$$\frac { 9 } { x + 9 } - \frac { 9 } { x - 9 }$$

Accepted Answer

A)  $\frac { 2 x ^ { 2 } } { x ^ { 2 } + 81 }$ 
B)  0 
C)  $\frac { 2 x ^ { 2 } - 162 } { x ^ { 2 } + 81 }$ 
D)  $\frac { - 162 } { x ^ { 2 } - 81 }$ 
A)  $\frac { 2 x ^ { 2 } } { x ^ { 2 } + 81 }$ 
B)  0 
C)  $\frac { 2 x ^ { 2 } - 162 } { x ^ { 2 } + 81 }$ 
D)  $\frac { - 162 } { x ^ { 2 } - 81 }$

Question 4

Find all numbers for which the rational expression is not defined.
-$$\frac { 9 } { b + 8 }$$

Accepted Answer

A)  $b = 0$ 
B)  None 
C)  $b = - 8$ 
D)  $b = 8$ 
A)  $b = 0$ 
B)  None 
C)  $b = - 8$ 
D)  $b = 8$

Question 5

Add. Simplify, if possible.
-$$\frac { 3 } { 14 x } + \frac { 9 } { 10 x ^ { 2 } }$$

Accepted Answer

A)  $\frac { 108 } { 70 x ^ { 2 } }$ 
B)  $\frac { 3 ( 5 x + 21 ) } { 70 x ^ { 2 } }$ 
C)  $\frac { 12 } { 140 x ^ { 2 } }$ 
D)  $\frac { 12 } { 14 x + 10 x ^ { 2 } }$ 
A)  $\frac { 108 } { 70 x ^ { 2 } }$ 
B)  $\frac { 3 ( 5 x + 21 ) } { 70 x ^ { 2 } }$ 
C)  $\frac { 12 } { 140 x ^ { 2 } }$ 
D)  $\frac { 12 } { 14 x + 10 x ^ { 2 } }$

Add. Simplify, if possible. - $\frac { 6 } { m - n ^ { 2 } } + \frac { 8 } { n ^ { 2 } - m }$

Divide and simplify. - $\frac { x ^ { 2 } - 25 } { x } \div \frac { 4 x + 20 } { x - 5 }$

Subtract. Simplify, if possible. - $\frac { 9 } { x + 9 } - \frac { 9 } { x - 9 }$

Find all numbers for which the rational expression is not defined. - $\frac { 9 } { b + 8 }$

Add. Simplify, if possible. - $\frac { 3 } { 14 x } + \frac { 9 } { 10 x ^ { 2 } }$

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

Finding Measures of Central Tendency for Prices and Heights

Filters

Exam 6: Rational Expressions and Equations

Add. Simplify, if possible. - 6m−n2+8n2−m\frac { 6 } { m - n ^ { 2 } } + \frac { 8 } { n ^ { 2 } - m }m−n26​+n2−m8​

Divide and simplify. - x2−25x÷4x+20x−5\frac { x ^ { 2 } - 25 } { x } \div \frac { 4 x + 20 } { x - 5 }xx2−25​÷x−54x+20​

Subtract. Simplify, if possible. - 9x+9−9x−9\frac { 9 } { x + 9 } - \frac { 9 } { x - 9 }x+99​−x−99​

Find all numbers for which the rational expression is not defined. - 9b+8\frac { 9 } { b + 8 }b+89​

Add. Simplify, if possible. - 314x+910x2\frac { 3 } { 14 x } + \frac { 9 } { 10 x ^ { 2 } }14x3​+10x29​