Exam 12: Rational Expressions and Equations

Solve the problem. -Martha can rake the leaves in her yard in 2 hours. Her younger brother can do the job in 7 hours. How long will it take them to do the job if they work together?

Find an equation of variation in which $y$ varies inversely as $x$ and the following is true. - $y=0.625$ , when $x=8$

Perform the indicated operation. Simplify, if possible. - $\frac{3 x+9}{x+2}+\frac{x+3}{x+4}-\frac{2 x+10}{(x+2)(x+4)}$

Solve the problem. -A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?

Solve the problem. -The distance $D$ that a spring is stretched by a hanging object varies directly as the weight $W$ of the object. If a $19-\mathrm{kg}$ object stretches a spring $10 \mathrm{~cm}$ , find the distance when the weight is $29-\mathrm{kg}$ .

Add. Simplify, if possible. - $\frac{2}{21 x}+\frac{4}{15 x^{2}}$

Divide and simplify. - $\frac{-12+4 x}{12} \div \frac{21-7 x}{21}$

Add. Simplify, if possible. - $\frac{x}{x^{2}-1}+\frac{4 x}{x-x^{2}}$

Subtract. Simplify, if possible. - $\frac{3 x}{x^{2}-25}-\frac{1}{5-x}$

Solve the equation. - $\frac{x-8}{x+2}=\frac{4}{9}$

For the pair of similar triangles, find the length of the indicated side. - In the upper triangle, the shortest side has length 16 , and the middle side has length 24 . In the lower triangle, the shortest side has length 12 , the middle side has length 18 , and the longest side has length 24. Find the length, $x$ , of the longest side of the upper triangle.

Simplify. - $\frac{\frac{1}{x^{2}}-\frac{4}{y^{2}}}{4 y-8 x}$

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

Simplify. - $\frac{y^{2}+3 y-18}{y^{2}+2 y-24}$

Divide and simplify. - $\frac{z^{2}+12 z+35}{z^{2}+14 z+49} \div \frac{z^{2}+5 z}{z^{2}+4 z-21}$

Solve the problem. -According to Ohm's law, the electric current $I$ , in amperes, in a circuit varies directly as the voltage $\mathrm{V}$ . When 20 volts are applied, the current is 3 amperes. What is the current when 10 volts are applied?

Divide and simplify. - $\frac{x^{2}+9 x+20}{x+4} \div \frac{x^{2}-25}{4 x-20}$

Subtract. Simplify, if possible. - $\frac{8}{7 x^{2}}-\frac{2}{7 x^{2}}$

Solve the equation. - $\frac{x+7}{x-2}=\frac{6}{2-x}$

Subtract. Simplify, if possible. - $\frac{3(y-1)}{5 y-3}-\frac{y-3}{3-5 y}-\frac{4 y}{5 y-3}$