Exam 7: Rational Expressions and Equations

Solve. -According to Ohmʹs law, the electric current, in amperes, in a circuit varies directly as the voltage. When 29 volts are applied, the current is 4 amperes. What is the current when 26 volts are applied?

Simplify the complex fraction. - $\frac { \frac { 9 } { x } - \frac { x } { 9 } } { \frac { 1 } { 9 } - \frac { 1 } { x } }$

For the given functions f(x) and g(x), find f(x) ∙ g(x). - $f ( x ) = \frac { x ^ { 2 } - 9 x + 18 } { x ^ { 2 } - 7 x + 12 } , g ( x ) = \frac { x ^ { 2 } + 3 x - 4 } { x ^ { 2 } - 7 x + 6 }$

Solve. -y varies directly as x. If y = 35 when x = 5 $\text { find } y \text { when } x$

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

Find all values of the variable for which the rational expression is undefined. - $\frac { x ^ { 2 } - 6 x - 16 } { x ^ { 2 } - 81 }$

Evaluate the rational expression for the given value of the variable - $\frac { x < 8 } { 6 x + 2 }$ for $x = - 2$

Add. - $\frac { 2 } { x ^ { 2 } - 3 x + 2 } + \frac { 7 } { x ^ { 2 } - 1 }$

Add. - $\frac { x ^ { 2 } - 5 x } { x ^ { 2 } + 6 x + 9 } + \frac { 4 x - 12 } { x ^ { 2 } + 6 x + 9 }$

Add. - $\frac { x } { x ^ { 2 } - 1 } + \frac { 6 x } { x - x ^ { 2 } }$

For the given functions f(x) and g(x), find f(x) ∙ g(x). - $f ( x ) = x - 5 , g ( x ) = \frac { x ^ { 2 } - 3 x - 10 } { 2 x ^ { 2 } - 5 x - 25 }$

Simplify the complex fraction. - $\frac { x + 2 + \frac { 1 } { x } } { x + 4 + \frac { 3 } { x } }$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { 3 x - 6 } { ( 4 + x ) ( 2 - x ) }$

For the given functions f(x) and g(x), find f(x) ∙ g(x). - $f ( x ) = \frac { x ^ { 2 } + 4 x + 4 } { x ^ { 2 } + 5 x + 6 } , g ( x ) = \frac { x ^ { 2 } + 3 x } { x ^ { 2 } + 7 x + 10 }$

Solve. -The sum of a number and 36 times its reciprocal is 12. Find the number.

Find the LCD of the given rational expressions. - $\frac { 8 } { x ^ { 2 } - 3 x } , \frac { 8 } { x ^ { 2 } + 3 x - 18 }$

Divide. - $\frac { x ^ { 2 } + 8 x + 12 } { x + 2 } \div \frac { x ^ { 2 } - 36 } { 2 x - 12 }$

Add. - $\frac { x ^ { 2 } - 8 x } { x - 7 } + \frac { 8 x - x ^ { 2 } } { x - 7 }$

Identify the given function as a linear function, a quadratic function, or a rational function. - $f ( x ) = \frac { 1 } { 5 } x ^ { 2 } - 64$

For the given rational functions f(x) and g(x), f(x) +g(x). - $f ( x ) = \frac { x } { x ^ { 2 } + 7 x - 8 } , g ( x ) = \frac { 8 } { x ^ { 2 } + 7 x - 8 }$