Exam 6: Rational Expressions and Equations

Solve. -The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00 , how much will a 7 foot length with diameter 5 inches cost?

Solve the equation. - $\frac { 23 } { x } = 8 - \frac { 1 } { x }$

Simplify. - $\frac { 12 - 8 x } { 2 x - 3 }$

For the pair of similar triangles, find the length of the indicated side. -In the outer triangle, the shortest side has length 12 , and the middle side has length 15 . In the inner triangle, the shortest side has length 4 , the middle side has length 5 , and the longest side has length 6 . Find the length, $x$ , of the longest side of the outer triangle.

Add, first finding the LCD. Simplify, if possible. - $\frac { 5 } { 24 } + \frac { 1 } { 54 }$

Find the equation of variation if the following is true. -Suppose that y varies directly as z and y = 40 when z = 240.

Multiply. Do not simplify. - $\frac { x + 5 } { x + 2 } \cdot \frac { x - 5 } { x - 5 }$

Solve. -The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 4 sec when the length is 64 inches, what is the period when L = 5.0625 inches?

Perform the indicated operation. Simplify, if possible. - $\frac { b } { b ^ { 2 } - 25 } + \frac { 5 } { b + 5 } - \frac { 6 } { b }$

Solve the equation. - $\frac { 3 } { y } = \frac { y } { 8 y - 45 }$

Divide and simplify. - $\frac { - 9 + 3 x } { 9 } \div \frac { 18 - 6 x } { 18 }$

Simplify. - $\frac { 5 + \frac { 1 } { 3 } } { 4 - \frac { 2 } { 27 } }$

Multiply and, if possible, simplify. - $\frac { x ^ { 4 } - 81 } { x ^ { 4 } - 16 } \cdot \frac { x ^ { 2 } + 4 } { x ^ { 2 } + 9 }$

Add. Simplify, if possible. - $\frac { 2 } { x - 7 } + \frac { 4 } { 7 - x }$

Solve. -According to Ohm's law, the electric current I, in amperes, in a circuit varies directly as the voltage V. When 7 volts are applied, the current is 2 amperes. What is the current when 6 volts are applied?

Add. Simplify, if possible. - $\frac { x } { x ^ { 2 } - 1 } + \frac { 7 x } { x - x ^ { 2 } }$

Subtract. Simplify, if possible. - $\frac { 7 } { 9 x ^ { 2 } } - \frac { 2 } { 9 x ^ { 2 } }$

Subtract. Simplify, if possible. - $\frac { 3 x + 28 } { x ^ { 2 } + 2 x - 8 } - \frac { x + 20 } { x ^ { 2 } + 2 x - 8 }$

Solve the problem. -The ratio of the weight of an object on Mars to the weight of an object on Earth is 0.4 to 1. How much will a 160-pound astronaut weigh on Mars?

Answer the question. -Explain why, when one number is a factor of another, the least common denominator of the numbers is the larger number.