Chapter 11

Simplify the expression. $$ \left(\frac{3 x^{2}}{56}\right)\left(\frac{3}{x}+\frac{5}{x}\right) $$

Factor first, then solve the equation. Check your solutions. \(\frac{1}{y^{2}-16}-\frac{2}{y+4}=\frac{2}{y-4}\)

Simplify the expression. $$ \frac{4}{x+4}-\frac{7}{5 x} $$

Write the quotient in simplest form. $$\frac{3 x+12}{4 x} \div \frac{x+4}{2 x}$$

Simplify the expression if possible. $$ \frac{12-5 x}{10 x^{2}-24 x} $$

Simplify the expression. $$ \left(\frac{3 x-5}{x}+\frac{1}{x}\right) \div\left(\frac{x}{6 x-8}\right) $$

Simplify the expression. $$ \frac{2 x+1}{3 x-1}-\frac{x+4}{x-2} $$

Write the quotient in simplest form. $$\frac{2 x^{2}+3 x+1}{12 x-12} \div \frac{x^{2}-1}{6 x}$$

Simplify the expression if possible. $$\frac{8 y^{2}-7 y}{14 y^{2}-16 y^{3}}$$

You are taking a trip on a highway in a car that gets a gas mileage of 26 miles per gallon for highway driving. You start with a full tank of 12 gallons of gasoline. Find your rate of gas consumption (gallons of gas used to drive 1 mile).

Solve the equation. Check your solutions. \(\frac{-3 x}{x+1}=\frac{-2}{x-1}\)

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

A scale model uses a scale of \(\frac{1}{16}\) inch to represent 1 foot. Explain how you can use a proportion and the cross product property to show that a scale of \(\frac{1}{16}\) in. to \(1 \mathrm{ft}\) is the same as a scale of 1 in. to 192 in.

Write the quotient in simplest form. $$\frac{x+5}{2+3 x} \div\left(x^{2}-25\right)$$

Simplify the expression if possible. $$ \frac{5-x}{x^{2}-8 x+15} $$

Solve the equation. Check your solutions. \(\frac{x}{6}-\frac{1}{x}=\frac{1}{6}\)

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

What are the extremes of the proportion \(\frac{1}{3}=\frac{x}{18} ?\) What are the extremes of \(\frac{x}{18}=\frac{1}{3} ?\) $$ \begin{array}{lllllllll} {\text { (A) }} {1,3 ; x, 18} & {} & {\text { (B) } x, 18 ; 1,3} & {} {\text { (C) } x, 3 ; 1,18} & {} {\text { (D) } 1,18 ; x, 3} \end{array} $$

Write the quotient in simplest form. $$\frac{x^{2}-36}{-5 x^{2}} \div(x-6)$$

Simplify the expression if possible. $$ \frac{9-2 y}{2 y^{2}-3 y-27} $$

Solve the equation. Check your solutions. \(\frac{x}{9}-\frac{8}{x}=\frac{1}{9}\)

Simplify the expression. $$ \frac{3 x+10}{7 x-4}-\frac{x}{4 x+3} $$

Solve \(\frac{x-2}{x+5}=\frac{x-5}{x+2}\) F. 1 G. \(-2\) and \(-5\) H. 2 and 5 J. No solution

Write the quotient in simplest form. $$\frac{x^{2}+19 x-20}{x^{2}} \div\left(x^{2}-1\right)$$

Simplify the expression if possible. $$ \frac{3 x-5}{25-30 x+9 x^{2}} $$

MULTIPLE CHOICE Assuming \(y=14\) when \(x=6,\) find an equation that relates \(x\) and \(y\) such that \(x\) and \(y\) vary directly. (A) \(x y=84\) (B) \(y=\frac{7}{3} x\) (C) \(y=\frac{3}{7} x\) (D) \(x y=\frac{7}{3}\)

Solve the equation. Check your solutions. \(\frac{x+42}{x}=x\)

In Exercises 43–45, use the following information. You are riding your bike to a pond that is 8 miles away. You have a choice to ride in the woods, on the road, or both. In the woods, you can ride at a speed of 10 mi/h. On the road, you can ride at a speed of 20 mi/h. Write an expression for your total time.

Solve \(\frac{c}{c-4}=\frac{8}{c-10}\). A. 0 B. 2 and 16 C. -18 and 32 D. No solution

Write the quotient in simplest form. $$\frac{y-12}{2 y+3} \div\left(y^{2}-14 y+24\right)$$

Find the quotient. $$\text { Divide }\left(a^{2}-3 a+2\right) \text { by }(a-1)$$

MULTIPLE CHOICE Assuming \(y=9\) when \(x=10,\) find an equation that relates \(x\) and \(y\) such that \(x\) and \(y\) vary inversely. $$ F) x y=90 $$ $$ G)y=\frac{9}{10} x $$ $$ H)y=\frac{10}{9} x $$ $$ J)x y=\frac{9}{10} $$

Solve the equation. Check your solutions. \(\frac{2}{x}-\frac{x}{8}=\frac{3}{4}\)

Write in point-slope form the equation of the line that passes through the given point and has the given slope. (Lesson 5.2) $$ (-1,-2), m=2 $$

Write the quotient in simplest form. $$\frac{3 x^{2}+2 x-8}{3 x} \div(3 x-4)$$

Find the quotient. $$\text { Divide }\left(5 g^{2}+13 g-6\right) \text { by }(g+3)$$

Evaluate. $$ 45 \% \text { of } 10 $$

Solve the equation. Check your solutions. \(\frac{-3}{x+7}=\frac{2}{x+2}\)

Use the following information. You are riding your bike to a pond that is 8 miles away. You have a choice to ride in the woods, on the road, or both. In the woods, you can ride at a speed of 10 mi/h. On the road, you can ride at a speed of 20 mi/h. Evaluate the expression for total time at 2 mile intervals.

Write in point-slope form the equation of the line that passes through the given point and has the given slope. (Lesson 5.2) $$ (5,-3), m=-4 $$

Write the quotient in simplest form. $$\frac{4 x+3}{x-1} \div\left(4 x^{2}+x-3\right)$$

Find the quotient. $$\text { Divide }\left(x^{2}-6 x-16\right) \text { by }(x+2)$$

Evaluate. $$ 30 \% \text { of } 42 $$

Which of the following expressions can be simplified to \(x+3 ?\) A. \(\frac{x^{2}}{x+3}-\frac{9}{x+3}\) B. \(\frac{x^{2}}{x-7}-\frac{4 x+21}{x-7}\) C. \(\frac{x-6}{x-3}-\frac{x+9}{x-3}\) D. None of these

Solve the equation. Check your solutions. \(\frac{2}{x+3}+\frac{1}{x}=\frac{4}{3 x}\)

In Exercises 46–48, use the following information. A boat moves through still water at x kilometers per hour (km/h). It travels 24 km upstream against a current of 2 km/h and then returns to the starting point with the current. The rate upstream is x-2 because the boat moves against the current, and the rate downstream is x 2 because the boat moves with the current. Write an algebraic model for the total time for the round trip.

Write in point-slope form the equation of the line that passes through the given point and has the given slope. (Lesson 5.2) $$ (-8,8), m=-1 $$

Find the quotient. $$ \text { Divide }\left(-5 m^{2}+25 m\right) \text { by } 5 m $$

Evaluate. $$ \frac{1}{2} \% \text { of } 200 $$

Simplify \(\frac{x^{2}}{x+5}-\frac{25}{x+5}\). F. \(\frac{1}{x-5}\) G. \(\frac{x^{2}-25}{x+5}\) H. \(x-5\) J. \(\frac{x-5}{x+5}\)