91影视

Use the \([\text { GRAPH }]\) or \([\text { TABLE }]\) feature of a graphing utility to determine if the rational expression has been correctly simplified. If the simplification is wrong, correct it and then verify your answer using the graphing utility. $$\frac{x^{2}-x}{x}=x^{2}-1, x \neq 0$$

Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. After adding rational expressions with different denominators, I factored the numerator and found no common factors in the numerator and denominator, so my final answer is incorrect if I leave the numerator in factored form.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$x-\frac{1}{5}=\frac{4}{5} x$$

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

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

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. $$\frac{2}{x}+1=\frac{2+x}{x}, x \neq 0$$

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

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