Exam 9: Rational Expressions

Simplify the complex fraction to eliminate fractions from the numerators and denominators. Assume there are no zero denominators. $\frac { x + \frac { x } { 5 } } { 5 - \frac { x } { 2 } }$

Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches 8. $y = - \frac { x + 8 } { ( x + 1 ) ( x - 8 ) }$

Find the least common denominator for the equation. $\frac { x } { 10 } + \frac { x } { 8 } = 12$

Simplify: $\frac { 4 r + 1 } { 3 r } - \frac { r - 4 } { 5 r }$

List 5 possible widths and lengths of rectangles with area of 36 square inches. Calculate the perimeter for each rectangle. Which is not true?

Find the least common denominator for the equation. $\frac { 1 } { 15 } + \frac { 1 } { x } = \frac { 1 } { 6 }$

Indicate any inputs that must be excluded and then solve the equation. Factoring of the quadratic equation may be helpful. $\frac { 5 } { 3 } + 4 x = \frac { 1 } { x }$

Add the rational expressions. Assume there are no zero denominators. $\frac { 13 } { x + 3 } + \frac { 3 x - 4 } { x + 3 }$

Multiply and divide fractions. Assume all denominators are nonzero. $\frac { t } { u } \text { and } \frac { v } { w }$

Multiply and divide the two fractions. $\frac { 1 } { 5 } \text { and } \frac { 1 } { 15 }$

Simplify: $\frac { 1 + \frac { 8 } { b } } { 1 - \frac { 64 } { b ^ { 2 } } }$

In economics, total quantity sold is the product of the price and the demand. Find the total quantity, Q. $\text { Price } = 4 x + 12 \quad \text { Demand } = \frac { 600 } { x ^ { 2 } + 3 x }$ Assume there are no zero denominators.

Estimated crude oil reserves in a certain year was about 1,100 billion barrels. If the average consumption of crude oil is x barrels per day, what equation describes how many days the oil reserves will last?

Add the fractions on the right side of the equals sign to obtain a single fraction for the application formula. Assume there are no zero denominators. Resistors in parallel in an electrical circuit: $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$

Indicate any inputs that must be excluded and then solve the equation. Factoring of the quadratic equation may be helpful. $x + 3 = \frac { x + 3 } { x }$

Find the missing number or expression in each pair of equivalent fraction. Assume there is no zero denominators. $\frac { 30 x } { 15 x ^ { 2 } } , \frac { 10 } { }$

Divide: $\frac { x ^ { 2 } - 4 x + 3 } { x ^ { 2 } - 6 x + 5 } \div \frac { x ^ { 2 } - 7 x + 12 } { x ^ { 2 } - 8 x + 15 }$

What inputs are defined for the expression? $\frac { 8 } { x - 7 }$

Simplify the fraction. $\frac { 6 - ( - 4 ) } { - 4 - 6 }$

Simplify: $\frac { 4 x ^ { 5 } y ^ { 2 } } { 9 x ^ { 3 } y ^ { 4 } }$