Exam 4: Rational Expressions

Perform the multiplication. Simplify the answer, if possible. $\frac { t z ^ { 2 } } { t ^ { 2 } z } \cdot \frac { 9 z ^ { 2 } a ^ { 2 } } { t z a } \div \frac { t z a ^ { 2 } } { t ^ { 3 } a ^ { 2 } }$

Kent drives his Mazda 270 miles in the same time that Dave drives his Nissan 250 miles. If Kent averages 4 miles per hour faster than Dave, find their rates.

Solve the proportion for the variable. $\frac { 6 } { y } = \frac { 9 } { 30 }$

Write the expression in lowest terms. If the expression is already in lowest terms, so indicate. Assume that the denominator does not equal zero. $\frac { x + 7 } { 9 ( x + 7 ) }$

A school board has determined that there should be 3 teachers for every 50 students. How many teachers are needed for an enrollment of 2,650 students?

Express the rational number in reduced form. $- \frac { 40 } { 50 }$

Perform the division. $\frac { 12 x - 3 y + 36 z } { 12 x y }$

Perform the multiplication. Simplify the answer, if possible. $\frac { 4 s a } { 7 z } \cdot \frac { 7 z a } { 3 s }$

Simplify the rational expression. $\frac { 8 x ^ { 2 } y + 24 x y ^ { 2 } - 32 y ^ { 3 } } { 48 x ^ { 3 } y - 36 x ^ { 2 } y ^ { 2 } - 12 x y ^ { 3 } }$

Do the addition. Simplify the result when possible. $\frac { 1 } { 9 } + \frac { 1 } { 27 }$

Express the rational number in reduced form. $\frac { 25 } { 30 }$

Perform the multiplication. Simplify the answer, if possible. $\frac { 2 s } { 5 y } \cdot \frac { 5 y } { 3 s }$

Perform the indicated division. $\frac { ( 2 x - 1 ) ^ { 2 } } { 200 x - 100 } \div \frac { 10 x ^ { 2 } + 3 x - 4 } { 10 x + 5 }$

Perform the indicated division and express your answer in simplest form. $\frac { 12 s a } { 3 s ^ { 2 } - 3 s a } \div \frac { s a + a } { 2 s - 2 a }$

Find the quotient. $\left( - \frac { 3 } { 5 } \right) \div \left( - \frac { 13 } { 10 } \right)$

Perform the operation. $\frac { 13 } { 3 } \left( - \frac { 18 } { 13 } \right)$