Exam 6: Rational Expression and Equations

Solve the problem by writing a variation model. The number of days that a given number of bushels of corn will last when feeding cattle varies inversely as the number of animals. If x bushels will feed 25 cows for 11 days, how long will the feed last for 11 cows? __________ days

Perform the operations and simplify the result when possible. $\frac { a + b } { 3 } + \frac { a - b } { 4 }$

Solve: $\frac { x ^ { 2 } } { 5 } = \frac { x } { 2 x - 9 }$

Perform the division. $\frac { 4 a ^ { 3 } + 9 a ^ { 2 } - 9 a + 8 } { a + 3 }$

Use synthetic division to perform the division. $\left( x ^ { 2 } - 4 x + 21 \right) \div ( x + 3 )$

Express the verbal model " b varies inversely with the cube of c " in symbols.

Use the remainder theorem and synthetic division to find P ( k ). $P ( x ) = x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 2 x + 5 ; k = - 1$

Use the remainder theorem and synthetic division to find $P ( - 2 )$ for $P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 3 x - 1$ . $P ( - 2 ) =$$\underline{\quad\quad}$

__________ division may be used if the divisor is of the form $x - k$

Simplify. Write the answer using positive exponents. $\frac { 2 x ^ { 2 } y ^ { 3 } } { 4 x ^ { 6 } y ^ { 2 } }$

Equations that contain one or more rational expressions, such as $\frac { 2 } { x } + \frac { 3 } { x - 1 } = 5$ , are called __________ equations.

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

It takes the owner/operator of a dog kennel 6 hr to clean all of the cages. It takes his assistant 2 hr more than that to clean the same cages. How long will it take if they work together? __________ hr

Perform the operations and simplify the result when possible. $\frac { 3 x + 4 } { x - 2 } - \frac { x - 12 } { 2 - x }$

Perform the division. $\frac { 16 x ^ { 2 } y ^ { 4 } + x ^ { 4 } y ^ { 2 } } { 8 x y }$

The powers of x in $2 x ^ { 4 } + 4 x ^ { 3 } + 5 x ^ { 2 } - 7 x - 8$ are written in __________ order.

Solve the formula for the indicated variable. $J = \frac { F } { \rho + p }$ for p

An aluminum brace used to support a wooden shelf has a length that is 3 inches less than twice the width of the shelf. The brace is anchored to the wall 3 inches below the shelf, as shown. Find the width of the shelf and the length of the brace. w = __________ in. l = __________ in.

To check the answer to a division problem, we use the fact that for any division: $\text { divisor } \cdot \text { quotient } + \text { remainder } =$$\underline{\quad\quad}$

One inlet pipe can fill an empty pool in 4 hours, and a drain can empty the pool in 6 hours. How long will it take the pipe to fill the pool if the drain is left open?