Chapter 7

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{6 y+18}{11 y+33}$$

Simplify complex rational expression by the method of your choice. \(\frac{x+9-\frac{7}{x}}{x-6+\frac{4}{x}}\)

Divide as indicated. $$\frac{x}{5} \div \frac{20}{x}$$

Solve each rational equation. $$\frac{10}{y+2}=3-\frac{5 y}{y+2}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{6 y^{2}+y}{2 y^{2}-9 y+9}-\frac{2 y+9}{2 y^{2}-9 y+9}-\frac{4 y-3}{2 y^{2}-9 y+9}$$

What is a proportion? Give an example with your description.

Factor: \(6 x^{3}-6 x^{2}-120 x\)

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x+1}{x^{2}-2 x-3}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{3}{x y^{2}}+\frac{2}{x^{2} y}}{\frac{1}{x^{2} y}+\frac{2}{x y^{3}}}\)

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

add or subtract as indicated. Simplify the result, if possible. $$\frac{3 y^{2}-2}{3 y^{2}+10 y-8}-\frac{y+10}{3 y^{2}+10 y-8}-\frac{y^{2}-6 y}{3 y^{2}+10 y-8}$$

What are similar triangles?

Evaluate \(\sqrt{x-1}\) for \(x=17\)

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x+2}{x^{2}-x-6}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{2}{x^{3} y}+\frac{5}{x y^{4}}}{\frac{5}{x^{3} y}-\frac{3}{x y}}\)

Divide as indicated. $$\frac{9}{x} \div \frac{3}{4 x}$$

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

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{4}{x-3}+\frac{2}{3-x}$$

If the ratio of the corresponding sides of two similar triangles is 1 to 1 ( \(\frac{1}{1}\) ), what must be true about the triangles?

Evaluate \(4 \sqrt{x}+30\) for \(x=25\)

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{4 x-8}{x^{2}-4 x+4}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{3}{x+1}-\frac{3}{x-1}}{\frac{5}{x^{2}-1}}\)

Add or subtract as indicated. Simplify the result, if possible. $$\frac{2 x}{x^{2}-16}+\frac{x}{x-4}$$

Divide as indicated. $$\frac{x+1}{3} \div \frac{3 x+3}{7}$$

Solve each rational equation. $$\frac{x+1}{3 x+9}+\frac{x}{2 x+6}=\frac{2}{4 x+12}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6}{x-5}+\frac{2}{5-x}$$

Describe how to identify the corresponding sides in similar triangles.

$$\text { Simplify: }(-2)^{5}-(-1)^{3}$$

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x^{2}-12 x+36}{4 x-24}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{3}{x+2}-\frac{3}{x-2}}{\frac{5}{x^{2}-4}}\)

Add or subtract as indicated. Simplify the result, if possible. $$\frac{4 x}{x^{2}-25}+\frac{x}{x+5}$$

Divide as indicated. $$\frac{x+1}{3} \div \frac{3 x+3}{7}$$

Solve each rational equation. $$\frac{3}{2 y-2}+\frac{1}{2}=\frac{2}{y-1}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6 x+7}{x-6}+\frac{3 x}{6-x}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve \(\frac{x}{9}=\frac{4}{6}\) by using the cross-products principle or by multiplying both sides by \(18,\) the least common denominator.

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{y^{2}-3 y+2}{y^{2}+7 y-18}$$

Simplify complex rational expression. \(\frac{\frac{6}{x^{2}+2 x-15}-\frac{1}{x-3}}{\frac{1}{x+5}+1}\)

Add or subtract as indicated. Simplify the result, if possible. $$\frac{5 y}{y^{2}-9}-\frac{4}{y+3}$$

Divide as indicated. $$\frac{7}{x-5} \div \frac{28}{3 x-15}$$

Solve each rational equation. $$\frac{4 y}{y^{2}-25}+\frac{2}{y-5}=\frac{1}{y+5}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6 x+5}{x-2}+\frac{4 x}{2-x}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve \(\frac{x}{9}=\frac{4}{6}\) by using the cross-products principle or by multiplying both sides by \(18,\) the least common denominator.

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{y^{2}+5 y+4}{y^{2}-4 y-5}$$

Simplify complex rational expression. \(\frac{\frac{1}{x-2}-\frac{6}{x^{2}+3 x-10}}{1+\frac{1}{x-2}}\)

Add or subtract as indicated. Simplify the result, if possible. $$\frac{8 y}{y^{2}-16}-\frac{5}{y+4}$$

Divide as indicated. $$\frac{4}{x-6}+\frac{40}{7 x-42}$$

Solve each rational equation. $$\frac{1}{x+4}+\frac{1}{x-4}=\frac{22}{x^{2}-16}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{5 x-2}{3 x-4}+\frac{2 x-3}{4-3 x}$$

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{2 y^{2}-7 y+3}{2 y^{2}-5 y+2}$$

Simplify complex rational expression. \(\frac{y^{-1}-(y+5)^{-1}}{5}\)