91Ó°ÊÓ

Find \(b\) so that the solution of \(\frac{7 x+4}{b}+13=x\) is \(-6.\)

Simplify each rational expression. $$\frac{16-y^{2}}{y(y-8)+16}$$

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

Use a graphing utility to solve each rational equation. Graph each side of the equation in the given viewing rectangle. The first coordinate of each point of intersection is a solution. Check by direct substitution. $$\begin{aligned} &\frac{x}{2}+\frac{x}{4}=6\\\ &[-5,10,1] \text { by }[-5,10,1] \end{aligned}$$

Simplify each rational expression. $$\frac{x y+2 y+3 x+6}{x^{2}+5 x+6}$$

Use a graphing utility to solve each rational equation. Graph each side of the equation in the given viewing rectangle. The first coordinate of each point of intersection is a solution. Check by direct substitution. $$\begin{aligned} &\frac{50}{x}=2 x\\\ &[-10,10,1] \text { by }[-20,20,2] \end{aligned}$$

When performing the division. $$\frac{7 x}{x+3} \div \frac{(x+3)^{2}}{x-5}$$ I began by dividing the numerator and the denominator by the common factor, \(x+3\)

Simplify each rational expression. $$\frac{x y+4 y-7 x-28}{x^{2}+11 x+28}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{7 x}{x^{2}-y^{2}}-\frac{3}{y-x}$$

After adding \(\frac{3 x+1}{4}\) and \(\frac{x+2}{4},\) I simplified the sum by dividing the numerator and the denominator by 4 I use similar procedures to find each of the following sums: $$ \frac{3}{8}+\frac{1}{8} \text { and } \frac{x}{x^{2}-1}+\frac{1}{x^{2}-1} $$