Chapter 11

Simplify. $$\frac{2-\frac{8}{x+4}}{3-\frac{12}{x+4}}$$

If a plane flies 300 mph in calm air and the rate of the wind is \(r\) miles per hour, then the rate of the plane flying with the wind can be represented as ______, and the rate of the plane flying against the wind can be represented as _______.

Simplify. $$\frac{6 y}{4 y+1}-\frac{11 y}{4 y+1}$$

Solve. $$\frac{x}{3}-\frac{1}{4}=\frac{x}{4}-\frac{1}{6}$$

Solve the formula for the given variable. $$F=\frac{9}{5} C+32 ; C \quad \text { (Temperature conversion) }$$

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

Find the LCM of the polynomials. $$\begin{aligned} &8 x^{2}(x-1)^{2}\\\ &10 x^{3}(x-1) \end{aligned}$$

Simplify. $$\frac{5-\frac{25}{x+5}}{1-\frac{3}{x+5}}$$

Suppose you have a powerboat with the throttle set to move the boat at 8 mph in calm water, and the rate of the current is \(4 \mathrm{mph}\). a. What is the speed of the boat when traveling with the current? \(\mathbf{b}\). What is the speed of the boat when traveling against the current?

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

Solve. $$\frac{2 y}{9}-\frac{1}{6}=\frac{y}{9}+\frac{1}{6}$$

Solve the formula for the given variable. $$A=\frac{1}{2} h\left(b_{1}+b_{2}\right) ; b_{1} \quad \text { (Geometry) }$$

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

Simplify. $$\frac{6 y(y+2)}{9 y^{2}(y+2)}$$

Simplify. $$\frac{1+\frac{5}{y-2}}{1-\frac{2}{y-2}}$$

The speed of a plane is 500 mph. There is a headwind of 50 mph. What is the speed of the plane relative to an observer on the ground?

Simplify. $$\frac{4 x+3}{2 x-7}+\frac{3 x-8}{2 x-7}$$

Solve. $$\frac{2 x-5}{8}+\frac{1}{4}=\frac{x}{8}+\frac{3}{4}$$

Solve the formula for the given variable. $$s=a(x-v t) ; t \quad \text { (Physics) }$$

Find the LCM of the polynomials. $$\begin{aligned} &4 x-12\\\ &2 x^{2}-12 x+18 \end{aligned}$$

Simplify. $$\frac{12 x^{2}(3-x)}{18 x(3-x)}$$

Simplify. $$\frac{2-\frac{11}{2 x-1}}{3-\frac{17}{2 x-1}}$$

Simplify. $$\frac{5 x-1}{x+9}-\frac{3 x+4}{x+9}$$

Solve the formula for the given variable. $$V=\frac{1}{3} A h ; h \quad \text { (Geometry) }$$

Solve. $$\frac{3 x+4}{12}-\frac{1}{3}=\frac{5 x+2}{12}-\frac{1}{2}$$

Find the LCM of the polynomials. $$\begin{aligned} &(x-1)(x+2)\\\ &(x-1)(x+3) \end{aligned}$$

Simplify. $$\frac{6 x(x-5)}{8 x^{2}(5-x)}$$

Simplify. $$\frac{4-\frac{2}{x+7}}{5+\frac{1}{x+7}}$$

Simplify. $$\frac{6 x-5}{x-10}-\frac{3 x-4}{x-10}$$

Solve. $$\frac{6}{2 a+1}=2$$

Solve the formula for the given variable. $$P=R-C ; C \quad \text { (Business) }$$

Find the LCM of the polynomials. $$\begin{aligned} &(2 x-1)(x+4)\\\ &(2 x+1)(x+4) \end{aligned}$$

Simplify. $$\frac{14 x^{3}(7-3 x)}{21 x(3 x-7)}$$

Simplify. $$\frac{5+\frac{3}{x-8}}{2-\frac{1}{x-8}}$$

A park has two sprinklers that are used to fill a fountain. One sprinkler can fill the fountain in \(3 \mathrm{h}\), whereas the second sprinkler can fill the fountain in \(6 \mathrm{h}\). How long will it take to fill the fountain with both sprinklers operating?

Simplify. $$\frac{x-7}{2 x+7}-\frac{4 x-3}{2 x+7}$$

Solve. $$\frac{12}{3 x-2}=3$$

Solve the formula for the given variable. $$R=\frac{C-S}{t} ; S \quad \text { (Business) }$$

Simplify. $$\frac{1-\frac{1}{x}-\frac{6}{x^{2}}}{1-\frac{9}{x^{2}}}$$

Find the LCM of the polynomials. $$\begin{array}{l} (2 x+3)^{2} \\ (2 x+3)(x-5) \end{array}$$

Simplify. $$\frac{a^{2}+4 a}{a b+4 b}$$

One grocery clerk can stock a shelf in 20 min. A second clerk requires 30 min to stock the same shelf. How long would it take to stock the shelf if the two clerks worked together?

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

Solve. $$\frac{9}{2 x-5}=-2$$

Solve the formula for the given variable. $$P=\frac{R-C}{n} ; R \quad \text { (Business) }$$

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

Find the LCM of the polynomials. $$\begin{aligned} &(x-7)(x+2)\\\ &(x-7)^{2} \end{aligned}$$

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

It takes Doug 6 days to reroof a house. If Doug's son helps him, the job can be completed in 4 days. How long would it take Doug's son, working alone, to do the job?

One person with a skiploader requires 12 h to transfer a large quantity of earth. With a larger skiploader, the same amount of earth can be transferred in \(4 \mathrm{h}\). How long would it take to transfer the earth if both skiploaders were operated together?