Chapter 11

Simplify. $$\frac{x}{x^{2}-9}+\frac{3}{x-3}$$

Divide. $$\frac{x^{2}-49}{x^{4} y^{3}} \div \frac{x^{2}-14 x+49}{x^{4} y^{3}}$$

Simplify. $$\frac{y}{y^{2}-16}+\frac{1}{y-4}$$

Divide. $$\frac{x^{2} y^{5}}{x^{2}-11 x+30} \div \frac{x y^{6}}{x^{2}-7 x+10}$$

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

Divide. $$\frac{4 a x-8 a}{c^{2}} \div \frac{2 y-x y}{c^{3}}$$

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

Divide. $$\frac{3 x^{2} y-9 x y}{a^{2} b} \div \frac{3 x^{2}-x^{3}}{a b^{2}}$$

Simplify. $$1-\frac{(y-2)^{2}}{(y+2)^{2}}$$

Divide. $$\frac{x^{2}-5 x+6}{x^{2}-9 x+18} \div \frac{x^{2}-6 x+8}{x^{2}-9 x+20}$$

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

Divide. $$\frac{x^{2}+3 x-40}{x^{2}+2 x-35} \div \frac{x^{2}+2 x-48}{x^{2}+3 x-18}$$

Simplify. $$\frac{y}{x-y}+2-\frac{x}{y-x}$$

Divide. $$\frac{x^{2}+2 x-15}{x^{2}-4 x-45} \div \frac{x^{2}+x-12}{x^{2}-5 x-36}$$

Simplify. $$\frac{3 x-1}{x^{2}-10 x+25}-\frac{3}{x-5}$$

Divide. $$\frac{y^{2}-y-56}{y^{2}+8 y+7} \div \frac{y^{2}-13 y+40}{y^{2}-4 y-5}$$

Simplify. $$\frac{2 a+3}{a^{2}-7 a+12}-\frac{2}{a-3}$$

Divide. $$\frac{8+2 x-x^{2}}{x^{2}+7 x+10} \div \frac{x^{2}-11 x+28}{x^{2}-x-42}$$

Simplify. $$\frac{x+4}{x^{2}-x-42}+\frac{3}{7-x}$$

Divide. $$\frac{x^{2}-x-2}{x^{2}-7 x+10} \div \frac{x^{2}-3 x-4}{40-3 x-x^{2}}$$

Simplify. $$\frac{x+3}{x^{2}-3 x-10}+\frac{2}{5-x}$$

Divide. $$\frac{2 x^{2}-3 x-20}{2 x^{2}-7 x-30} \div \frac{2 x^{2}-5 x-12}{4 x^{2}+12 x+9}$$

Simplify. $$\frac{1}{x+1}+\frac{x}{x-6}-\frac{5 x-2}{x^{2}-5 x-6}$$

Divide. $$\frac{6 n^{2}+13 n+6}{4 n^{2}-9} \div \frac{6 n^{2}+n-2}{4 n^{2}-1}$$

Simplify. $$\frac{x}{x-4}+\frac{5}{x+5}-\frac{11 x-8}{x^{2}+x-20}$$

State whether the given division is equivalent to \(\frac{x^{2}-3 x-4}{x^{2}+5 x-6}\). $$\frac{x-4}{x+6} \div \frac{x-1}{x+1}$$

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

State whether the given division is equivalent to \(\frac{x^{2}-3 x-4}{x^{2}+5 x-6}\). $$\frac{x+1}{x+6} \div \frac{x-1}{x-4}$$

Simplify. $$\frac{4 x+1}{x-8}-\frac{3 x+2}{x+4}-\frac{49 x+4}{x^{2}-4 x-32}$$

State whether the given division is equivalent to \(\frac{x^{2}-3 x-4}{x^{2}+5 x-6}\). $$\frac{x+1}{x-1} \div \frac{x+6}{x-4}$$

Simplify. $$\frac{2 x+9}{3-x}+\frac{x+5}{x+7}-\frac{2 x^{2}+3 x-3}{x^{2}+4 x-21}$$

State whether the given division is equivalent to \(\frac{x^{2}-3 x-4}{x^{2}+5 x-6}\). $$\frac{x-1}{x+1} \div \frac{x-4}{x+6}$$

Simplify. $$\frac{3 x+5}{x+5}-\frac{x+1}{2-x}-\frac{4 x^{2}-3 x-1}{x^{2}+3 x-10}$$

Name the values of \(x\) for which the rational expression is undefined. (Hint: Set the denominator equal to zero and solve for \(x\).) $$\frac{x}{(x-2)(x+5)}$$

Rewrite the expression as the sum of two fractions in simplest form. $$\frac{5 b+4 a}{a b}$$

Name the values of \(x\) for which the rational expression is undefined. (Hint: Set the denominator equal to zero and solve for \(x\).) $$\frac{x+5}{x^{2}-4 x-5}$$

Rewrite the expression as the sum of two fractions in simplest form. $$\frac{6 x+7 y}{x y}$$

Name the values of \(x\) for which the rational expression is undefined. (Hint: Set the denominator equal to zero and solve for \(x\).) $$\frac{3 x-8}{3 x^{2}-10 x-8}$$

Rewrite the expression as the sum of two fractions in simplest form. $$\frac{3 x^{2}+4 x y}{x^{2} y^{2}}$$

Rewrite the expression as the sum of two fractions in simplest form. $$\frac{2 m n^{2}+8 m^{2} n}{m^{3} n^{3}}$$

Suppose that you drive about \(12,000 \mathrm{mi}\) per year and that the cost of gasoline averages 3.70 dollar per gallon. a. Let \(x\) represent the number of miles per gallon your car gets. Write a variable expression for the amount you spend on gasoline in one year. b. Write and simplify a variable expression for the amount of money you will save each year if you increase your gas mileage by 5 miles per gallon. c. If you currently get 25 miles per gallon and you increase your gas mileage by 5 miles per gallon, how much will you save in one year?

Given the expression \(\frac{9}{x^{2}+1},\) choose some values of \(x\) and evaluate the expression for those values. Is it possible to choose a value of \(x\) for which the value of the expression is greater than \(10 ?\) If so, give such a value. If not, explain why it is not possible.

Given the expression \(\frac{1}{y-3},\) choose some values of \(y\) and evaluate the expression for those values. Is it possible to choose a value of \(y\) for which the value of the expression is greater than \(10,000,000 ?\) If so, give such a value. If not, explain why it is not possible.