91Ó°ÊÓ

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{-1}{x+4}+\frac{4}{7 x-1} $$

Set up an algebraic equation and solve each problem. What number must be added to the numerator and denominator of \(\frac{2}{5}\) to produce a rational number that is equivalent to \(\frac{7}{8} ?\)

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{-3}{4 x+3}+\frac{5}{2 x-5} $$

For problems \(53-64\), use synthetic division to determine the quotient and remainder. $$ \left(x^{2}-10 x+15\right) \div(x-8) $$

Last week Al bought some golf balls for $$\$ 20$$. The next day they were on sale for $$\$ 0.50$$ per ball less, and he bought \(\$ 22.50\) worth of balls. If he purchased 5 more balls on the second day than on the first day, how many did he buy each day and at what price per ball?

Simplify each complex fraction. $$ \frac{\frac{3}{n-5}-2}{1-\frac{4}{n-5}} $$

For Problems 51-58, simplify each rational expression. You will need to use factoring by grouping. \(\frac{x^{2}+3 x+4 x+12}{2 x^{2}+6 x-x-3}\)

Simplify each complex fraction. $$ \frac{\frac{-1}{y-2}+\frac{5}{x}}{\frac{3}{x}-\frac{4}{x y-2 x}} $$

Use synthetic division to determine the quotient and remainder. $$ \left(x^{3}-2 x^{2}-x+2\right) \div(x-2) $$

Set up an algebraic equation and solve each problem. A 20-foot board is to be cut into two pieces whose lengths are in the ratio of 7 to 3 . Find the lengths of the two pieces.