Exam 12: Rational Expressions and Equations

Multiply and, if possible, simplify. - $\frac{\mathrm{k}^{2}+5 \mathrm{k}+6}{\mathrm{k}^{2}+11 \mathrm{k}+18} \cdot \frac{\mathrm{k}^{2}+9 \mathrm{k}}{\mathrm{k}^{2}+12 \mathrm{k}+27}$

Find an equation of variation in which $y$ varies inversely as $x$ and the following is true. - $y=0.6$ , when $x=0.9$

Solve the problem. -Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 216 miles in the same time that Dana travels 192 miles. If Chuck's rate of travel is $4 \mathrm{mph}$ more than Dana's, and they travel the same length of time, at what speed does Chuck travel?

Solve the problem. -The volume $V$ of a gas varies inversely as the pressure $P$ on it. The volume of a gas is $300 \mathrm{~cm}^{3}$ under a pressure of $31 \mathrm{~kg} / \mathrm{cm}^{2}$ . Find an equation of variation.

Multiply and, if possible, simplify. - $\frac{x^{4}-81}{x^{4}-1} \cdot \frac{x^{2}+1}{x^{2}+9}$

For the pair of similar triangles, find the length of the indicated side. - In the outer triangle, the shortest side has length 6 , and the middle side has length 9 . In the inner triangle, the shortest side has length 2 , the middle side has length 3 , and the longest side has length 4 . Find the length, $x$ , of the longest side of the outer triangle.

Add. Simplify, if possible. - $\frac{m+3}{m^{2}-4 m+3}+\frac{4 m-1}{m^{2}-5 m+6}$

Solve the problem. -The amount of money that Pablo makes in a given week varies directly as the number of hours he works that week. In a week in which he works 28 hours, he makes $\$ 504$ . How much will he make in a week in which he works 44 hours?

Add. Simplify, if possible. - $\frac{7}{(x+5)^{2}}+\frac{2}{x+5}$

Add. Simplify, if possible. - $\frac{6}{x-3}+\frac{4}{3-x}$

Solve the equation. - $\frac{-5 x}{3 x+18}=\frac{7 x}{6 x+36}+\frac{6 x-1}{x+6}$

Solve the equation. - $\frac{x}{x+5}-\frac{5}{x-5}=\frac{x^{2}+25}{x^{2}-25}$

Solve the equation. - $\frac{-1}{y+5}-\frac{8}{y-5}=\frac{10}{y^{2}-25}$

Divide and simplify. - $\frac{3 x^{2}}{4} \div \frac{x^{3}}{16}$

Subtract. Simplify, if possible. - $\frac{3 x+24}{x^{2}-3 x-18}-\frac{x+18}{x^{2}-3 x-18}$

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

Multiply. Do not simplify. - $\frac{x+4}{x+9} \cdot \frac{x-4}{x-4}$

Divide and simplify. - $\frac{10}{y-x} \div \frac{5}{x-y}$

Perform the indicated operation. Simplify, if possible. - $\frac{5 x}{x-8}-\frac{6 x-2}{8-x}-\frac{2 x}{x-8}$

Find the LCM. - $8 x y, 12 x^{2}$