Chapter 11

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

Solve. $$\frac{6}{4-3 x}=3$$

Solve the formula for the given variable. $$A=P+P r ; P \quad \text { (Business) }$$

Simplify. $$\frac{1-\frac{5}{x}-\frac{6}{x^{2}}}{1+\frac{6}{x}+\frac{5}{x^{2}}}$$

Find the LCM of the polynomials. $$\begin{aligned} &x-1\\\ &x-2\\\ &(x-1)(x-2) \end{aligned}$$

Simplify. $$\frac{4-6 x}{3 x^{2}-2 x}$$

Simplify. $$\frac{3 x}{x^{2}+3 x-10}-\frac{6}{x^{2}+3 x-10}$$

Solve. $$2+\frac{5}{x}=7$$

Solve the formula for the given variable. $$T=f m-g m ; m \quad \text { (Engineering) }$$

Simplify. $$\frac{1-\frac{7}{a}+\frac{12}{a^{2}}}{1+\frac{1}{a}-\frac{20}{a^{2}}}$$

Find the LCM of the polynomials. $$\begin{aligned} &(x+4)(x-3)\\\ &x+4\\\ &x-3 \end{aligned}$$

Simplify. $$\frac{5 x y-3 y}{9-15 x}$$

One computer can solve a complex prime factorization problem in 75 h. A second computer can solve the same problem in 50 h. How long would it take both computers, working together, to solve the problem?

Simplify. $$\frac{2 x+3}{x^{2}-x-30}-\frac{x-2}{x^{2}-x-30}$$

Solve. $$3+\frac{8}{n}=5$$

Solve the formula for the given variable. $$A=S w+w ; w \quad \text { (Physics) }$$

Simplify. $$\frac{1-\frac{6}{x}+\frac{8}{x^{2}}}{\frac{4}{x^{2}}+\frac{3}{x}-1}$$

Find the LCM of the polynomials. $$\begin{aligned} &x^{2}-x-6\\\ &x^{2}+x-12 \end{aligned}$$

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

A new machine makes 10.000 aluminum cans three times faster than an older machine. With both machines operating, it takes \(9 \mathrm{h}\) to make \(10,000\) cans. How long would it take the new machine, working alone, to make \(10,000\) cans?

Simplify. $$\frac{3 x-1}{x^{2}+5 x-6}-\frac{2 x-7}{x^{2}+5 x-6}$$

Solve. $$1-\frac{9}{x}=4$$

Solve the formula for the given variable. \(a=S-S r ; S \quad\) (Mathematics)

Find the LCM of the polynomials. $$\begin{aligned} &x^{2}+3 x-10\\\ &x^{2}+5 x-14 \end{aligned}$$

Simplify. $$\frac{1+\frac{3}{x}-\frac{18}{x^{2}}}{\frac{21}{x^{2}}-\frac{4}{x}-1}$$

Simplify. $$\frac{x^{2}+5 x+6}{x^{2}+8 x+15}$$

A small air conditioner can cool a room \(5^{\circ} \mathrm{F}\) in 60 min. A larger air conditioner can cool the room \(5^{\circ} \mathrm{F}\) in 40 min. How long would it take to cool the room \(5^{\circ} \mathrm{F}\) with both air conditioners working?

Simplify. $$\frac{4 y+7}{2 y^{2}+7 y-4}-\frac{y-5}{2 y^{2}+7 y-4}$$

Solve. $$3-\frac{12}{x}=7$$

For Exercises 21 to \(32,\) solve for \(y\). $$3 x+y=10$$

Find the LCM of the polynomials. $$\begin{aligned} &x^{2}+5 x+4\\\ &x^{2}-3 x-28 \end{aligned}$$

Simplify. $$\frac{x^{2}+3 x-10}{x^{2}+2 x-8}$$

Simplify. $$\frac{x-\frac{4}{x+3}}{1+\frac{1}{x+3}}$$

One printing press can print the first edition of a book in 55 min. A second printing press requires 66 min to print the same number of copies. How long would it take to print the first edition of the book with both presses operating?

Simplify. $$\frac{x+1}{2 x^{2}-5 x-12}+\frac{x+2}{2 x^{2}-5 x-12}$$

Solve. $$\frac{2}{y}+5=9$$

For Exercises 21 to \(32,\) solve for \(y\). $$2 x+y=5$$

Find the LCM of the polynomials. $$\begin{aligned} &x^{2}-10 x+21\\\ &x^{2}-8 x+15 \end{aligned}$$

Simplify. $$\frac{a^{2}+7 a-8}{a^{2}+6 a-7}$$

Simplify. $$\frac{y+\frac{1}{y-2}}{1+\frac{1}{y-2}}$$

Two welders working together can complete a job in 6 h. One of the welders, working alone, can complete the task in 10 h. How long would it take the second welder, working alone, to complete the task?

Simplify. $$\frac{2 x^{2}+3 x}{x^{2}-9 x+20}+\frac{2 x^{2}-3}{x^{2}-9 x+20}-\frac{4 x^{2}+2 x+1}{x^{2}-9 x+20}$$

Solve. $$\frac{6}{x}+3=11$$

For Exercises 21 to \(32,\) solve for \(y\). $$4 x-y=3$$

Find the LCM of the polynomials. $$\begin{aligned} &x^{2}-2 x-24\\\ &x^{2}-36 \end{aligned}$$

Simplify. $$\frac{x^{2}+x-12}{x^{2}-6 x+9}$$

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

Working together, Pat and Chris can reseal a driveway in 6 h. Working alone, Pat can reseal the driveway in 15 h. How long would it take Chris, working alone, to reseal the driveway?

Simplify. $$\frac{2 x^{2}+3 x}{x^{2}-2 x-63}-\frac{x^{2}-3 x+21}{x^{2}-2 x-63}-\frac{x-7}{x^{2}-2 x-63}$$

Solve. $$\frac{3}{x-2}=\frac{4}{x}$$