Chapter 11

Write the sum in simplest form. $$ \frac{11}{6 x}+\frac{2}{13 x} $$

Solve the proportion using the cross product property. Check your solution. $$ \frac{3}{10}=\frac{1}{10 a} $$

Write the product in simplest form. $$\frac{c^{2}-64}{4 c^{3}} \cdot \frac{c}{c^{2}+9 c+8}$$

Simplify the expression. If not possible, write already in simplest form. $$\frac{t^{4}}{t^{2}(t+2)}$$

FACTORING AFTER ADDING OR SUBTRACTING. Simplify the expression. $$ \frac{x}{x^{2}+5 x-24}+\frac{8}{x^{2}+5 x-24} $$

The variables \(x\) and \(y\) vary inversely. Use the given values to write an equation that relates \(x\) and \(y .\) $$ x=1.5, y=50 $$

Solve the equation by multiplying each side by the least common denominator. Check your solutions. \(\frac{3}{t}-\frac{1}{3 t}=\frac{2}{3}\)

Write the sum in simplest form. $$ \frac{9}{4 x}+\frac{7}{-5 x} $$

Solve the equation. Check your solutions. $$ \frac{z}{9}=\frac{4}{z} $$

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

Simplify the expression. If not possible, write already in simplest form. $$ \frac{10(r-6)}{10 r} $$

FACTORING AFTER ADDING OR SUBTRACTING. Simplify the expression. $$ \frac{a^{2}-2}{a^{2}-25}+\frac{4 a-3}{a^{2}-25} $$

The variables \(x\) and \(y\) vary inversely. Use the given values to write an equation that relates \(x\) and \(y .\) $$ x=45, y=0.6 $$

Solve the equation by multiplying each side by the least common denominator. Check your solutions. \(\frac{4}{x(x+1)}=\frac{3}{x}\)

Write the sum in simplest form. $$ \frac{2 x+3}{4}+\frac{x+1}{2} $$

Solve the equation. Check your solutions. $$ \frac{4}{p}=\frac{p}{16} $$

Write the product in simplest form. $$\frac{3 x}{x+4} \cdot(3 x+12)$$

Simplify the expression. If not possible, write already in simplest form. $$\frac{7 x}{12 x+x^{2}}$$

FACTORING AFTER ADDING OR SUBTRACTING. Simplify the expression. $$ \frac{2 x}{x^{2}+5 x+4}+\frac{8}{x^{2}+5 x+4} $$

The variables \(x\) and \(y\) vary inversely. Use the given values to write an equation that relates \(x\) and \(y .\) $$ x=10.5, y=7 $$

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

Write the sum in simplest form. $$ \frac{3}{12 m^{3}}+\frac{m+1}{4 m^{3}} $$

Solve the equation. Check your solutions. $$ \frac{x+6}{3}=\frac{x-5}{2} $$

Write the product in simplest form. $$\frac{7 x-15}{11 x+121} \cdot(x+11)$$

Simplify the expression. If not possible, write already in simplest form. $$ \frac{3 x^{2}-18 x}{-9 x^{2}} $$

FACTORING AFTER ADDING OR SUBTRACTING. Simplify the expression. $$ \frac{x^{2}-10}{x^{2}-4}+\frac{3 x}{x^{2}-4} $$

DIRECT OR INVERSE VARIATION Make a table of values for \(x=-4,-3\) \(-2,-1,1,2,3,\) and \(4 .\) Use the table to sketch the graph. State whether \(x\) and \(y\) vary directly or inversely. $$ y=\frac{4}{x} $$

Solve the equation by multiplying each side by the least common denominator. Check your solutions. \(\frac{1}{s}+\frac{s}{s+2}=1\)

Write the sum in simplest form. $$ \frac{3 n}{15}+\frac{n^{2}+1}{30 n} $$

Solve the equation. Check your solutions. $$ \frac{x-2}{4}=\frac{x+10}{10} $$

Write the product in simplest form. $$(y-3)^{2} \cdot \frac{2 y-2}{y^{2}-4 y+3}$$

Simplify the expression. If not possible, write already in simplest form. $$ \frac{42 x-6 x^{3}}{36 x} $$

FACTORING AFTER ADDING OR SUBTRACTING. Simplify the expression. $$ \frac{2 x}{x^{2}+5 x}-\frac{x}{x^{2}+5 x} $$

DIRECT OR INVERSE VARIATION Make a table of values for \(x=-4,-3\) \(-2,-1,1,2,3,\) and \(4 .\) Use the table to sketch the graph. State whether \(x\) and \(y\) vary directly or inversely. $$ y=\frac{3 x}{2} $$

Solve the equation by multiplying each side by the least common denominator. Check your solutions. \(\frac{2}{3 x+1}+2=\frac{2}{3}\)

Write the difference in simplest form. $$ \frac{2 x}{5}-\frac{x+1}{4} $$

Solve the equation. Check your solutions. $$ \frac{r+4}{3}=\frac{r}{5} $$

Write the product in simplest form. $$\left(x^{2}+2 x+1\right) \cdot \frac{x+2}{x^{2}+3 x+2}$$

Simplify the expression. If not possible, write already in simplest form. $$ \frac{x^{2}+25}{2 x+10} $$

FACTORING AFTER ADDING OR SUBTRACTING. Simplify the expression. $$ \frac{2 x(x+4)}{(x+1)^{2}}-\frac{3 x-3}{(x+1)^{2}} $$

DIRECT OR INVERSE VARIATION Make a table of values for \(x=-4,-3\) \(-2,-1,1,2,3,\) and \(4 .\) Use the table to sketch the graph. State whether \(x\) and \(y\) vary directly or inversely. $$ y=3 x $$

Solve the equation by multiplying each side by the least common denominator. Check your solutions. \(\frac{5}{2 r+1}-\frac{3}{2 r-1}=0\)

Write the difference in simplest form. $$ \frac{9}{2 x}-\frac{2}{7 x^{2}} $$

Solve the equation. Check your solutions. $$ \frac{5}{2 y}=\frac{7}{y-3} $$

Write the product in simplest form. $$\frac{2 x+3}{2 x^{2}-3 x-9} \cdot\left(x^{2}-9\right)$$

Simplify the expression. If not possible, write already in simplest form. $$\frac{2(5-d)}{2(d-5)}$$

FACTORING AFTER ADDING OR SUBTRACTING. Simplify the expression. $$ \frac{y^{2}-2 y}{y^{2}-7 y-18}-\frac{9(y-2)}{y^{2}-7 y-18} $$

DIRECT OR INVERSE VARIATION Make a table of values for \(x=-4,-3\) \(-2,-1,1,2,3,\) and \(4 .\) Use the table to sketch the graph. State whether \(x\) and \(y\) vary directly or inversely. $$ y=\frac{6}{x} $$

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

Write the difference in simplest form. $$ \frac{3}{6 b^{2}}-\frac{1}{4 b} $$