Exam 6: Rational Expressions and Equations

Answer the question. -In the given problem $\frac { 16 ( y - 3 ) } { 4 ( y - 5 ) } \div \frac { ? } { ( y - 5 ) ( y + 9 ) } = \frac { 4 ( y + 9 ) } { ( y + 3 ) }$ , what must be the polynomial that is represented by the question mark?

Simplify. - $\frac { 15 \mathrm { k } ^ { 3 } } { 5 \mathrm { k } }$

Find all numbers for which the rational expression is not defined. -x2 - 16 x2 - 16x + 63

Find an equation of variation in which y varies inversely as x and the following is true. - $y = 0.3 \text {, when } x = 0.4$

Simplify. - $\frac { \frac { 1 } { x ^ { 2 } } - \frac { 16 } { y ^ { 2 } } } { 5 y - 20 x }$

Simplify. - $\frac { \frac { 2 } { 2 x ^ { 3 } } - \frac { 3 } { 8 x } } { \frac { 3 } { 4 x } + \frac { 3 } { 2 x ^ { 3 } } }$

Simplify. - $\frac { 2 x + 2 } { 10 x ^ { 2 } + 16 x + 6 }$

Simplify. - $\frac { 2 m ^ { 2 } + 2 m } { 14 m ^ { 2 } + 4 m }$

Add, first finding the LCD. Simplify, if possible. - $\frac { 2 } { 3 } + \frac { 5 } { 9 } + \frac { 3 } { 4 }$

Find all numbers for which the rational expression is not defined. - $\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 3 x - 10 }$

Perform the indicated operation. Simplify, if possible. - $\frac { 36 x } { 7 ( 6 x + 1 ) } - \frac { 1 } { 7 x ( 6 x + 1 ) } + \frac { 1 } { x }$

Solve the equation. - $\frac { 4 } { y + 2 } - \frac { 6 } { y - 2 } = \frac { 14 } { y ^ { 2 } - 4 }$

Divide and simplify. - $\frac { x ^ { 2 } - 9 } { x } \div \frac { 7 x + 21 } { x - 3 }$

Find the LCM. -90, 18, 45

Simplify. - $\frac { \frac { 1 } { a } + 1 } { \frac { 1 } { a } - 1 }$

Solve. -The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 5-m beam can support 280 kg. How many kilograms can a 1-m beam support?

For the pair of similar triangles, find the length of the indicated side. -In the upper triangle, the shortest side has length 12 , and the middle side has length 18 . In the lower triangle, the shortest side has length 8 , the middle side has length 12 , and the longest side has length 16 . Find the length, $x$ , of the longest side of the upper triangle.

Subtract. Simplify, if possible. - $\frac { 14 x y } { x ^ { 2 } - y ^ { 2 } } - \frac { x - y } { x + y }$

Subtract. Simplify, if possible. - $\frac { 6 } { x + 6 } - \frac { 6 } { x - 6 }$

Divide and simplify. - $\frac { x ^ { 2 } + 6 x + 8 } { x + 2 } \div \frac { x ^ { 2 } - 16 } { 2 x - 8 }$