Exam 12: Rational Expressions and Equations

Solve the problem. -A force is applied to a spring in order to compress it. The distance the spring is compressed from its natural length is denoted by $x$ , and the force applied varies directly as $x$ . If a force of $35 \mathrm{~N}$ compresses the spring by $1.0 \mathrm{~m}$ , then what force is required to compress the spring by $1.8 \mathrm{~m}$ ?

Add. Simplify, if possible. - $\frac{9}{8 x^{2}}+\frac{3}{8 x^{2}}$

Subtract. Simplify, if possible. - $\frac{\mathrm{r}}{\mathrm{r}-\mathrm{s}}-\frac{\mathrm{r}}{\mathrm{r}+\mathrm{s}}$

Find the LCM. - $n, 8+n, 8-n$

Find the LCM. -20,15

Solve the problem. -Maria and Charlie can deliver 44 papers in 4 hours. How long would it take them to deliver 33 papers?

Find an equation of variation in which $y$ varies inversely as $x$ and the following is true. - $y=5$ , when $x=20$

Solve the equation. - $\frac{1}{\mathrm{y}+3}-\frac{8}{\mathrm{y}-3}=\frac{8}{\mathrm{y}^{2}-9}$

Find the reciprocal. - $\frac{t+8}{t-4}$

Solve the equation. - $\frac{2}{t}=\frac{t}{3 t-4}$

Simplify. - $\frac{3 m^{2}+3 m}{15 m^{2}+21 m}$

Simplify. - $\frac{16 m^{2} p^{2}}{8 m^{9} p}$

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

Find all numbers for which the rational expression is not defined. - $\frac{x^{2}-36}{x^{2}-13 x+42}$

Find the ratio. Simplify, if possible. -A machine can fill 1064 boxes of cereal in 0.2 hour. How many boxes of cereal can it fill per hour?

Solve the equation. - $\frac{9}{m-2}-\frac{6}{m+2}=\frac{6}{m^{2}-4}$

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

Solve the problem. -The interest I earned in $1 \mathrm{yr}$ on a fixed principal varies directly as the interest rate $\mathrm{r}$ . An investment earns $\$ 25.38$ at an interest rate of $3.55 \%$ . Find an equation of variation.

Add. Simplify, if possible. - $\frac{m^{2}-10 m}{m-6}+\frac{24}{m-6}$