Chapter 11

Explain the meaning of the phrase "rate of work."

Determine whether the statement is true or false. To add two fractions, add the numerators and the denominators.

For Exercises 1 and \(2,\) determine whether the statement is true or false. Literal equations are solved using the same properties of equations that are used to solve equations in one variable.

Exercises 1 to 3 are the examples of complex fractions given at the beginning of Objective 11.4A. By what fraction would you multiply each complex fraction in order to simplify it? $$\frac{3}{2-\frac{1}{2}}$$

The process of clearing denominators in an equation containing fractions is an application of which property of equations?

What is a rational expression? Provide an example.

Fill in the blank to make a true statement. If it takes a janitorial crew \(5 \mathrm{h}\) to clean a company's offices, then in \(x\) hours the crew has completed ______ of the job.

Determine whether the statement is true or false. The procedure for subtracting two rational expressions is the same as that for subtracting two arithmetic fractions.

For Exercises 1 and \(2,\) determine whether the statement is true or false. In solving a literal equation, the goal is to get the variable being solved for alone on one side of the equation and all numbers and other variables on the other side of the equation.

Exercises 1 to 3 are the examples of complex fractions given at the beginning of Objective 11.4A. By what fraction would you multiply each complex fraction in order to simplify it? $$\frac{4+\frac{1}{x}}{3+\frac{2}{x}}$$

If the denominator of a fraction is \(x+3,\) for what value of \(x\) is the fraction undefined?

When is a rational expression in simplest form?

Determine whether the statement is true or false. To add two rational expressions, first multiply both expressions by the LCD.

In solving \(I=\frac{E}{R+r}\) for \(R,\) the goal is to get alone on one side of the equation.

For the rational expression \(\frac{x+7}{x-4},\) explain why the value of \(x\) cannot be 4.

Fill in the blank to make a true statement. Two people completed a job. If one person completed \(\frac{t}{30}\) of the job and the other person completed \(\frac{t}{20}\) of the job, then \(\frac{t}{30}+\frac{t}{20}=\) _________.

$$\text { If } x \neq-2 \text { and } x \neq 0, \text { then } \frac{x}{x+2}+\frac{3}{x+2}=\frac{x+3}{x+2}=\frac{3}{2}$$

In solving \(L=a(1+c t)\) for \(c,\) the goal is to get alone on one side of the equation.

Determine whether the statement is true or false. To simplify a complex fraction, multiply the complex fraction by the LCM of the denominators of the fractions in the numerator and denominator of the complex fraction.

After solving an equation containing fractions, why must we check the solution?

Determine whether the statement is true or false. We can rewrite \(\frac{x}{y}\) as \(\frac{4 x}{4 y}\) by using the Multiplication Property of One.

If Jen can paint a wall in 30 min and Amelia can paint the same wall in 45 min, who has the greater rate of work?

Simplify. $$\frac{3}{y^{2}}+\frac{8}{y^{2}}$$

Solve the formula for the given variable. $$d=r t ; t \quad \text { (Physics) }$$

State the values of \(x\) that would result in division by zero when substituted into the original equation. $$\frac{6 x}{x+1}-\frac{x}{x-2}=4$$

Find the LCM of the polynomials. $$\begin{aligned} &8 x^{3} y\\\ &12 x y^{2} \end{aligned}$$

Determine whether the statement is true or false. When we multiply the numerator and denominator of a complex fraction by the same expression, we are using the Multiplication Property of One.

Simplify. $$\frac{9 x^{3}}{12 x^{4}}$$

It takes Pat \(3 \mathrm{h}\) to mow the lawn. a. What is Pat's rate of work? b. What fraction of the lawn can Pat mow in 2 h?

Simplify. $$\frac{6}{a b}-\frac{2}{a b}$$

Solve the formula for the given variable. $$E=I R ; R \quad \text { (Physics) }$$

Find the LCM of the polynomials. $$\begin{aligned} &6 a b^{2}\\\ &18 a b^{3} \end{aligned}$$

Simplify. $$\frac{16 x^{2} y}{24 x y^{3}}$$

Determine whether the statement is true or false. Our goal in simplifying a complex fraction is to rewrite it so that there are no fractions in the numerator or in the denominator. We then express the fraction in simplest form.

Simplify. $$\frac{3}{x+4}-\frac{10}{x+4}$$

Solve the formula for the given variable. $$P V=n R T ; T \quad \text { (Chemistry) }$$

Simplify. $$\frac{(x+3)^{2}}{(x+3)^{3}}$$

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

Find the LCM of the polynomials. $$\begin{array}{l} 2 x^{2} y \\ 3 x^{2}+12 x \end{array}$$

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

Solve. $$\frac{2 x}{3}-\frac{5}{2}=-\frac{1}{2}$$

Solve the formula for the given variable. \(A=b h ; h \quad\) (Geometry)

Simplify. $$\frac{(2 x-1)^{5}}{(2 x-1)^{4}}$$

Find the LCM of the polynomials. $$\begin{aligned} &4 x y^{2}\\\ &6 x y^{2}+12 y^{2} \end{aligned}$$

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

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

Solve. $$\frac{x}{3}-\frac{1}{4}=\frac{1}{12}$$

Solve the formula for the given variable. $$P=2 l+2 w ; l \quad \text { (Geometry) }$$

Simplify. $$\frac{3 n-4}{4-3 n}$$

Find the LCM of the polynomials. $$\begin{aligned} &9 x(x+2)\\\ &12(x+2)^{2} \end{aligned}$$