Chapter 6

Perform the indicated operations. When possible write down only the answer. $$\frac{5 x}{2} \div 3$$

Solve each problem. If two receivers with resistances \(R_{1}\) and \(R_{2}\) are connected in parallel, then the formula relates the total resistance for the circuit \(R\) with \(R_{1}\) and \(R_{2}\). Given that \(R_{1}\) is 3 ohms and \(R\) is 2 ohms, find \(R_{2}\) $$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$$

Simplify. $$\frac{a^{-2}+b^{-2}}{a^{-1} b}$$

Reduce each rational expression to its lowest terms. $$\frac{2 a b+2 b y+3 a+3 y}{2 b^{2}-7 b-15}$$

Solve each equation. $$\frac{y}{3}=\frac{4}{3}-\frac{1}{y}$$

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

Reduce each rational expression to its lowest terms. $$\frac{3 m^{2}+3 m n+m+n}{12 m^{2}-5 m-3}$$

Solve each equation. $$\frac{1}{2 x-4}+\frac{1}{x-2}=\frac{1}{4}$$

Perform the indicated operations. When possible write down only the answer. $$\frac{3}{4} \div \frac{1}{4}$$

The thin lens equation relates the object distance \(S_{o},\) the image distance \(S_{i,}\) and the focal length \(F\) for a thin lens. If the object distance is \(500 \mathrm{mm}\) and the focal length is \(100 \mathrm{mm},\) then what is the image distance? $$ \frac{1}{S_{o}}+\frac{1}{S_{i}}=\frac{1}{F} $$

Reduce each rational expression to its lowest terms. $$\frac{4 x^{2}-10 x-6}{2 x^{2}+11 x+5}$$

Solve each equation. $$\frac{7}{3 x-9}-\frac{1}{x-3}=\frac{4}{9}$$

Perform the indicated operations. When possible write down only the answer. $$\frac{1}{4} \div \frac{1}{2}$$

Simplify. $$m^{-1}-a^{-1}$$

Reduce each rational expression to its lowest terms. $$\frac{6 x^{2}+x-1}{8 x^{2}-2 x-3}$$

Office party. A group of coworkers are planning to share the 1000 dollars cost of an office party. If they can get three more people to join them in sharing the cost, then the cost per person will go down by 75 dollars. How many workers are in the original group?

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

Convert each rational expression into an equivalent rational expression that has the indicated denominator. $$ \frac{1}{5}, \frac{?}{50} $$

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

Solve each problem. Sailing party. A group of sailors is planning to share equally the cost of a 40,000 dollars sailboat. When two sailors dropped out of the group, the cost per sailor increased by 1000 dollars . How many sailors were in the original group?

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

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

Perform the indicated operations. When possible write down only the answer. $$\text { One-half of } \frac{4 x}{3}$$

Simplify. $$\frac{2 m^{-1}-3 m^{-2}}{m^{-2}}$$

Solve each equation. $$\frac{5}{2 w+6}-\frac{1}{w-1}=\frac{1}{w+3}$$

Perform the indicated operations. When possible write down only the answer. One-third of \(\frac{6 x}{y}\)

Solve each problem. White-water rafting. Adventures, Inc., has a \(\$ 1500\) group rate for an overnight rafting trip on the Colorado River. For the last trip five people failed to show, causing the price per person to increase by \(\$ 25 .\) How many were originally scheduled for the trip?

Simplify. $$\frac{4 x^{-3}-6 x^{-5}}{2 x^{-5}}$$

Solve each equation. $$\frac{5}{x-3}=\frac{x}{x-3}$$

Perform the indicated operations. When possible write down only the answer. $$(a-b) \div(b-a)$$

Solve each problem. Muffy can eat a 25 -pound bag of dog food in 28 days, whereas Missy eats a 25 -pound bag in 23 days. How many days would it take them together to finish a 50 -pound bag of dog food.

Simplify. $$\frac{a^{-1}-b^{-1}}{a-b}$$

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

Perform the indicated operations. When possible write down only the answer. $$\left(x^{2}-y^{2}\right) \div\left(y^{2}-x^{2}\right)$$

Solve each problem. Rodent food. A pest control specialist has found that 6 rats can eat an entire box of sugar-coated breakfast cereal in 13.6 minutes, and it takes a dozen mice 34.7 minutes to devour the same size box of cereal. How long would it take all 18 rodents, in a cooperative manner, to finish off a box of cereal?

Solve each equation. $$\frac{w}{6}=\frac{3}{2 w}$$

Perform the indicated operations. When possible write down only the answer. $$(a-b) \div(-1)$$

Solve each equation. $$\frac{2 m}{5}=\frac{10}{m}$$

Perform the indicated operations. When possible write down only the answer. $$\left(x^{2}+y^{2}\right) \div(-1)$$

Convert each rational expression into an equivalent rational expression that has the indicated denominator. $$\frac{x}{x-3}, \frac{?}{x^{2}-9}$$

Solve each equation. $$\frac{5}{4 x-2}-\frac{1}{1-2 x}=\frac{7}{3 x+6}$$

Perform the indicated operations. When possible write down only the answer. $$\frac{x-y}{3} \cdot \frac{6}{y-x}$$

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

Convert each rational expression into an equivalent rational expression that has the indicated denominator. $$\frac{1}{2 x+2}, \frac{?}{-6 x-6}$$

Solve each equation. $$\frac{5}{x+1}-\frac{1}{1-x}=\frac{1}{x^{2}-1}$$

Perform the indicated operations. When possible write down only the answer. $$\frac{5 x-5 y}{x} \cdot \frac{1}{x-y}$$

Simplify. $$\frac{a+27 a^{-2}}{1-3 a^{-1}+9 a^{-2}}$$

Solve each equation. $$\frac{5}{x}=\frac{2}{5}$$

Perform the indicated operations. When possible write down only the answer. $$\frac{2 a+2 b}{a} \cdot \frac{1}{2}$$

Simplify. $$\left(x^{-1}+y^{-1}\right)^{-1}$$