Exam 7: Rational Expressions and Equations

Simplify the complex fraction. - $\mathrm { S } = \frac { \mathrm { H } } { \mathrm { m } \left( \mathrm { t } _ { 1 } - \mathrm { t } _ { 2 } \right) }$ for $\mathrm { t } _ { 2 }$

Simplify the complex fraction. - $\frac { \frac { 1 } { x } - 2 } { \frac { 1 } { x } + 5 }$

Solve the problem. - $\text { eff takes } 5 \text { hours longer to build a fence than it takes Bill. When they work together, it takes them }$

Determine whether the two binomials are or are not opposites. -x - 4 and 4 - x

Subtract. - $\frac { 4 x ^ { 2 } - 9 x - 5 } { x ^ { 2 } + 6 x } - \frac { 3 x ^ { 2 } - 3 x - 5 } { x ^ { 2 } + 6 x }$

Find the missing numerator and denominator. - $\frac { ( x - 10 ) ( x - 8 ) } { ( x - 4 ) ( x - 7 ) } \cdot \frac { ? } { ? } = \frac { ( x - 8 ) ( x - 11 ) } { ( x - 4 ) ( x - 2 ) }$

Divide. - $\frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 15 x + 54 } \div \frac { x ^ { 2 } + 2 x } { x ^ { 2 } + 14 x + 48 }$

Subtract. - $\frac { 6 } { x ^ { 2 } } - \frac { 5 } { x }$

Divide. - $\frac { ( 2 x - 7 ) ( x + 1 ) } { ( x + 6 ) ( x - 4 ) } \div \frac { ( x + 1 ) ( 3 x + 7 ) } { ( x + 6 ) ( x - 4 ) }$

Solve. -The sum of a number and 10 times its reciprocal is -7. Find the number.

Solve the problem. -A water tank can be filled in 5 minutes and emptied in 8 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

Subtract. - $\frac { 12 x } { x ^ { 2 } - 36 } - \frac { x } { x - 6 }$

Divide. - $\frac { x ^ { 2 } - 25 } { x ^ { 2 } + 18 x + 81 } \div \frac { 4 x - 20 } { x ^ { 2 } + 12 x + 27 }$

Solve the problem. -A jet plane moving at constant speed travels 1000 miles with the wind and then 1200 miles against the wind. If the speed of the wind is 50 mph and the total flight takes 5 hours, find the speed of the Plane.

For the given rational functions f(x) and g(x), f(x) +g(x). - $f ( x ) = \frac { 6 } { x } , g ( x ) = \frac { 3 } { x }$

Find the missing numerator. - $\frac { ? } { x - 5 } - \frac { 25 } { x - 5 } = 5$

Add or subtract. - $\frac { 4 x } { x - 1 } + \frac { 4 } { 1 - x }$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { x ^ { 2 } - 2 x } { ( x + 4 ) ( x - 2 ) }$

Add. - $\frac { 15 } { x - 8 } + \frac { 11 } { x - 8 }$

For the given functions f(x) and g(x), find f(x) ∙ g(x). - $f ( x ) = \frac { x ^ { 2 } + 13 x + 42 } { x ^ { 2 } + 14 x + 49 } , g ( x ) = \frac { x ^ { 2 } + 7 x } { x ^ { 2 } - 3 x - 54 }$