Chapter 11

Solve the equation by cross multiplying. Check your solutions. \(\frac{6}{x+2}=\frac{x}{4}\)

Find the missing numerator. $$ \frac{11}{3 x}=\frac{2}{12 x^{3}} $$

Solve the proportion using the cross product property. Check your solution. $$ \frac{x}{3}=\frac{7}{3} $$

Write the product in simplest form. $$\frac{3 x}{x^{2}-2 x-24} \cdot \frac{x-6}{6 x^{2}}$$

Simplify the expression. If not possible, write already in simplest form. $$\frac{4 x}{20}$$

ADDING RATIONAL EXPRESSIONS. Simplify the expression. $$ \frac{2 x}{4 x+6}+\frac{3}{4 x+6} $$

The variables \(x\) and \(y\) vary directly. Use the given values to write an equation that relates \(x\) and \(y .\) $$ x=27, y=3 $$

Solve the equation by cross multiplying. Check your solutions. \(\frac{5}{x+4}=\frac{5}{3(x+1)}\)

Find the missing numerator. $$ \frac{8}{5}=\frac{?}{15 y^{2}} $$

Solve the proportion using the cross product property. Check your solution. $$ \frac{16}{4}=\frac{12}{z} $$

Write the product in simplest form. $$\frac{z^{2}+8 z+7}{10 z} \cdot \frac{z^{2}}{z^{2}-49}$$

Simplify the expression. If not possible, write already in simplest form. $$\frac{45 x}{15}$$

SUBTRACTING RATIONAL EXPRESSIONS. Simplify the expression. $$ \frac{7 x}{x^{3}}-\frac{6 x}{x^{3}} $$

The variables \(x\) and \(y\) vary inversely. Use the given values to write an equation that relates \(x\) and \(y .\) $$ x=2, y=5 $$

Solve the equation by cross multiplying. Check your solutions. \(\frac{1}{y}=\frac{2}{y-3}\)

Find the missing numerator. $$ \frac{x-3}{2}=\frac{?}{28 x} $$

Solve the proportion using the cross product property. Check your solution. $$ \frac{42}{28}=\frac{3}{x} $$

Write the product in simplest form. $$\frac{5-2 x}{6} \cdot \frac{24}{10-4 x}$$

Simplify the expression. If not possible, write already in simplest form. $$\frac{-18 x^{2}}{12 x}$$

SUBTRACTING RATIONAL EXPRESSIONS. Simplify the expression. $$ \frac{8+6 t}{3 t}-\frac{5 t-6}{3 t} $$

The variables \(x\) and \(y\) vary inversely. Use the given values to write an equation that relates \(x\) and \(y .\) $$ x=3, y=7 $$

Solve the equation by cross multiplying. Check your solutions. \(\frac{3\left(t^{2}+1\right)}{6 t^{2}-t-1}=\frac{1}{2}\)

Find the missing numerator. $$ \frac{3 a+1}{9 a^{5}}=\frac{?}{63 a^{11}} $$

Solve the proportion using the cross product property. Check your solution. $$ \frac{5}{y}=\frac{8}{9} $$

Write the product in simplest form. $$\frac{3 a}{a+4} \cdot \frac{a^{2}+5 a+4}{a^{2}+a}$$

Simplify the expression. If not possible, write already in simplest form. $$\frac{14 x^{2}}{50 x^{4}}$$

SUBTRACTING RATIONAL EXPRESSIONS. Simplify the expression. $$ \frac{2 x}{x+2}-\frac{2 x+1}{x+2} $$

The variables \(x\) and \(y\) vary inversely. Use the given values to write an equation that relates \(x\) and \(y .\) $$ x=16, y=1 $$

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

Find the missing numerator. $$ \frac{x-9}{2 x+3}=\frac{?}{x(2 x+3)} $$

Solve the proportion using the cross product property. Check your solution. $$ \frac{4}{2 w}=\frac{7}{3} $$

Write the product in simplest form. $$\frac{3 x^{2}-6 x}{2 x+1} \cdot \frac{4 x+2}{x-2}$$

Simplify the expression. If not possible, write already in simplest form. $$\frac{10 x^{5}}{16 x^{3}}$$

SUBTRACTING RATIONAL EXPRESSIONS. Simplify the expression. $$ \frac{2}{3 x-1}-\frac{5 x}{3 x-1} $$

The variables \(x\) and \(y\) vary inversely. Use the given values to write an equation that relates \(x\) and \(y .\) $$ x=11, y=2 $$

Solve the equation by multiplying each side by the least common denominator. Check your solutions. \(\frac{5}{x}+2=\frac{x}{4}\)

Find the missing numerator. $$ \frac{2 a-3}{35 a^{2}}=\frac{?}{140 a^{5}} $$

Solve the proportion using the cross product property. Check your solution. $$ \frac{5}{3 d}=\frac{2}{3} $$

Write the product in simplest form. $$\frac{x}{x-2} \cdot \frac{x^{2}-3 x+2}{x-1}$$

Simplify the expression. If not possible, write already in simplest form. $$\frac{36 x}{27 x}$$

SUBTRACTING RATIONAL EXPRESSIONS. Simplify the expression. $$ \frac{4 x}{2 x+6}-\frac{16}{2 x+6} $$

The variables \(x\) and \(y\) vary inversely. Use the given values to write an equation that relates \(x\) and \(y .\) $$ x=\frac{1}{2}, y=8 $$

Solve the equation by multiplying each side by the least common denominator. Check your solutions. \(\frac{x}{x+9}=\frac{9}{x+9}+4\)

Write the sum in simplest form. $$ \frac{3}{2 z}+\frac{1}{z} $$

Solve the proportion using the cross product property. Check your solution. $$ \frac{14}{3}=\frac{7 b}{2} $$

Write the product in simplest form. $$\frac{45 x^{3}-9 x^{2}}{x} \cdot \frac{2}{6(x-5)}$$

Simplify the expression. If not possible, write already in simplest form. $$\frac{x-14}{x}$$

SUBTRACTING RATIONAL EXPRESSIONS. Simplify the expression. $$ \frac{4 m}{m-2}-\frac{2 m+4}{m-2} $$

The variables \(x\) and \(y\) vary inversely. Use the given values to write an equation that relates \(x\) and \(y .\) $$ x=5, y=\frac{13}{5} $$

Solve the equation by multiplying each side by the least common denominator. Check your solutions. \(\frac{3 x}{x-1}=\frac{x}{5}\)