Exam 6: Rational Expression and Equations

A rectangle has a width of 1 meter and length of x meters. When a square with sides 1 meter in length is removed, the remaining rectangle has sides in the same ratio as the original rectangle. What is the exact value of x ?

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = x ^ { 3 } + x ^ { 2 } + 10 ; k = - 3$

Perform the operations and simplify the result when possible. $\frac { a + b } { 2 } + \frac { a - b } { 7 }$

Use synthetic division to perform the division. $\left( 4 x ^ { 3 } - 1 + 5 x ^ { 2 } \right) \div ( x + 2 )$

The expression $\frac { x - 7 } { 4 x }$ is a binomial divided by a __________.

Perform the operations and simplify the result when possible. $- \frac { x + 10 } { 2 x ^ { 2 } - 11 x + 5 } + \frac { 3 x - 5 } { x ^ { 2 } - 4 x - 5 }$

Solve: $\frac { x + 3 } { x } = \frac { x } { x + 6 }$

Perform the division. $\frac { 8 a ^ { 3 } - 16 a ^ { 2 } + 9 } { 2 a - 3 }$

Divide using synthetic division: $\frac { x ^ { 3 } - 8 x ^ { 2 } + 2 } { x + 2 }$

Multiply, then simplify if possible. $16 x \left( \frac { x + 4 } { 4 x } \right)$

Perform the division. $\frac { 10 x ^ { 3 } - 7 x ^ { 2 } - 10 x - 3 } { 2 x - 3 }$

Perform the indicated operation. Simplify, if possible. $\frac { 4 x - 1 } { x ^ { 2 } - 3 x - 10 } - \frac { x } { x ^ { 2 } - 4 }$

In a scale drawing, a 280-foot antenna tower is drawn $7 \frac { 1 } { 2 }$ inches high. The building next to it is drawn $2 \frac { 1 } { 4 }$ inches high. How tall is the actual building?

Use the remainder theorem and synthetic division to find $P ( - 2 )$ for $P ( x ) = 3 x ^ { 3 } + 4 x - 5$ .

Subtract, and then simplify, if possible. $\frac { 10 } { a + 4 } - \frac { 14 } { a + 3 }$

The __________ of $\frac { x - 8 } { x + 7 }$ and $\frac { 6 - 5 x } { x }$ is $x ( x + 7 )$ .

Complete the table using the formula $r \cdot t = d$ . rate time distance Running x 15 Bicycling x+20 15

Perform the indicated operation. Simplify, if possible. $\frac { x ^ { 2 } - 8 x - 9 } { x ^ { 2 } + x - 6 } \div \frac { x ^ { 2 } - 12 x + 27 } { x ^ { 2 } - 4 x - 21 } \cdot \frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 6 x - 7 }$

Use synthetic division to perform the division. $\frac { 2 x ^ { 3 } - 8 - 4 x } { x - 2 }$

Perform the indicated operation. Simplify, if possible. $\frac { 2 x ^ { 2 } + 7 x - 4 } { 3 x ^ { 2 } + 8 x - 16 } \div \frac { 2 x ^ { 2 } + 3 x - 2 } { 3 x + 6 }$