Chapter 11

Explain what is meant by the least common denominator of two rational expressions.

Describe the shape of a hyperbola. What is an asymptote of a hyperbola?

Write the extremes and the means of the proportion \(\frac{3}{4}=\frac{9}{12}\).

How is polynomial long division like long division with whole numbers? How is it different?

Describe the steps used to multiply two rational expressions.

Define a rational expression. Then give an example of a rational expression.

Write an equation that represents the statement "10\% of 160 is 16." What is the base number?

What does it mean for two quantities to vary directly? to vary inversely?

Find the least common denominator. $$\frac{1}{x}, \frac{x}{3}, \frac{2}{3 x}$$

Write yes or no to tell whether the equation is a consequence of \(\frac{a}{b}=\frac{c}{d}\). $$ a c=b d $$

Describe the steps used to divide two rational expressions.

The sale price of a shirt is \(\$ 17.25\) after a \(25 \%\) discount is taken. The sale price is what percent of the regular price?

You can use \(x-3\) as the LCD when finding the sum \(\frac{5}{x-3}+\frac{2}{3-x}\) What number can you multiply the numerator and the denominator of the second fraction by to get an equivalent fraction with \(x-3\) as the new denominator?

Find the least common denominator. $$\frac{3}{4 x}, \frac{1}{6 x^{2}}, \frac{1}{8 x^{2}}$$

Write yes or no to tell whether the equation is a consequence of \(\frac{a}{b}=\frac{c}{d}\). $$b a=d c$$

The sale price of a shirt is \(\$ 17.25\) after a \(25 \%\) discount is taken. You can model the situation with an equation of the form \(a\) is \(p\) percent of \(b\). Is the base \(b\) the sale price or the regular price?

Simplify the expression. $$\frac{1}{3 x}+\frac{5}{3 x}$$

Find the least common denominator. $$\frac{1}{x^{2}+6 x+9}, \frac{1}{x+3}$$

Write yes or no to tell whether the equation is a consequence of \(\frac{a}{b}=\frac{c}{d}\). $$a d=b c$$

For what values of the variable is the rational expression undefined? $$\frac{6}{8 x}$$

Simplify the expression. $$\frac{3 x}{8 x^{2}} \cdot \frac{4 x^{3}}{3 x^{4}}$$

The sale price of a shirt is \(\$ 17.25\) after a \(25 \%\) discount is taken. Write and solve an equation to find the regular price of the shirt.

Simplify the expression. $$\frac{5 x}{x+4}+\frac{20}{4+x}$$

Divide \(y^{2}+8\) by \(y+2\)

For what values of the variable is the rational expression undefined? $$\frac{x-1}{x-5}$$

Simplify the expression. $$\frac{x^{2}-1}{x} \cdot \frac{2 x}{3 x-3}$$

One student says that the equation \(y=-2 x\) is an example of direct variation. Another student says it is inverse variation. Which is correct? Explain.

Simplify the expression. $$\frac{x}{x^{2}-9}-\frac{3 x+1}{x^{2}-9}$$

Solve the equation. Remember to check for extraneous solutions. $$\frac{3}{x}=\frac{x}{12}$$

Write yes or no to tell whether the equation is a consequence of \(\frac{a}{b}=\frac{c}{d}\). $$\frac{b}{a}=\frac{d}{c}$$

Set up the long division problem, but do not perform the division. Divide \(-x^{2}-4 x+21\) by \(-x+3\)

For what values of the variable is the rational expression undefined? $$\frac{2}{x^{2}-x-2}$$

Solve the percent problem. \(12 \%\) of 5 is what number?

Simplify the expression. $$\frac{x}{x^{2}-25} \cdot \frac{x-5}{x+5}$$

Does the equation model direct variation, inverse variation, or neither? $$x=\frac{4}{y}$$

Simplify the expression. $$\frac{3}{10 x}-\frac{1}{4 x^{2}}$$

Solve the equation. Remember to check for extraneous solutions. $$\frac{-4 x}{x+1}=\frac{2}{x-2}$$

Which of the following is the simplified form of \(\frac{6+2 x}{x^{2}+5 x+6} ?\) $$\text { A. } \frac{2 x}{x^{2}+5 x}$$ $$\text { B. } \frac{2}{x+5}$$ $$\text { C. } \frac{2}{x+2}$$

Set up the long division problem, but do not perform the division. Divide \(8 y^{2}-2 y\) by \(3 y+5\)

Simplify the expression. $$\frac{3 x}{x^{2}-2 x-15} \cdot(x+3)$$

Solve the percent problem. 18 is \(37.5 \%\) of what number?

Does the equation model direct variation, inverse variation, or neither? $$y=7 x-2$$

Simplify the expression. $$\frac{x+6}{x+1}-\frac{4}{2 x+3}$$

Solve the equation. Remember to check for extraneous solutions. $$\frac{x}{6}+\frac{15}{x}=\frac{5}{6}$$

Solve the proportion \(\frac{4}{x+1}=\frac{7}{2}\) two ways- using the reciprocal property and using the cross product method. Which method do you prefer? Why?

Set up the long division problem, but do not perform the division. Divide \(72-18 x+x^{2}\) by \(x-6\)

Solve the percent problem. 13.2 is \(120 \%\) of what number?

Simplify the expression. $$\frac{x}{8-2 x} \div \frac{2 x}{4-x}$$

Does the equation model direct variation, inverse variation, or neither? $$a=12 b$$

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