Chapter 7

Multiply: \(\frac{5}{6} \cdot \frac{9}{25} .\) (Section 1.2, Example 5)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The LCD of \(\frac{1}{x}\) and \(\frac{2 x}{x-1}\) is \(x^{2}-1\)

Divide: \(\frac{2}{3} \div 4 .\) (Section 1.2, Example 6)

Solve by the addition method: $$\left\\{\begin{array}{l}2 x-5 y=-2 \\\3 x+4 y=20 . \text { (Section 4.3, Example 3)}\end{array}\right.$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{2}{x}+1=\frac{2+x}{x}, x \neq 0$$

This will help you prepare for the material covered in the next section. In each exercise, perform the indicated operation. $$\frac{2}{5} \cdot \frac{3}{7}$$

Perform the indicated operations. Simplify the result, if possible. $$\frac{y^{2}+5 y+4}{y^{2}+2 y-3} \cdot \frac{y^{2}+y-6}{y^{2}+2 y-3}-\frac{2}{y-1}$$

This will help you prepare for the material covered in the next section. In each exercise, perform the indicated operation. $$\frac{3}{4} \div \frac{1}{2}$$

Perform the indicated operations. Simplify the result, if possible. $$\left(\frac{1}{x+h}-\frac{1}{x}\right) \div h$$

This will help you prepare for the material covered in the next section. In each exercise, perform the indicated operation. $$\frac{5}{4} \div \frac{15}{8}$$

Find the missing rational expression. $$\frac{4}{x-2}-\frac{2 x+8}{(x-2)(x+1)}$$

Multiply: \(\quad(3 x+5)(2 x-7) .\) (Section 5.3, Example 2)

Graph: \(3 x-y<3 .\) (Section 3.6, Example 2)

Write the slope-intercept form of the equation of the line passing through \((-3,-4)\) and \((1,0) .\) (Section 3.5 Example 2 )

Will help you prepare for the material covered in the next section. a. Add: \(\frac{1}{3}+\frac{2}{5}\) b. Subtract: \(\frac{2}{5}-\frac{1}{3}\) c. Use your answers from parts (a) and (b) to find \(\left(\frac{1}{3}+\frac{2}{5}\right) \div\left(\frac{2}{5}-\frac{1}{3}\right)\)

Will help you prepare for the material covered in the next section. a. Add: \(\frac{1}{x}+\frac{1}{y}\) b. Use your answer from part (a) to find \(\frac{1}{x y} \div\left(\frac{1}{x}+\frac{1}{y}\right)\)

Will help you prepare for the material covered in the next section. Multiply and simplify: \(\quad x y\left(\frac{1}{x}+\frac{1}{y}\right)\)