91Ó°ÊÓ

Find$R\left(x\right)=f\left(x\right)-g\left(x\right)$where$f\left(x\right)=\frac{x+1}{x+3}$and$g\left(x\right)=\frac{x+17}{x^2-x-12}$.

Find$R\left(x\right)=f\left(x\right)+g\left(x\right)$where$f\left(x\right)=\frac{x-4}{x+3}$and$g\left(x\right)=\frac{4x+6}{x^2-9}$.

Simplify the complex rational expression by writing it as a division:

$\frac{{\displaystyle \frac{2}{x^2-1}}}{{\displaystyle \frac{3}{x+1}}}$

Simplify the complex rational expression by writing it as division:

$\frac{{\displaystyle \frac{1}{x^2-7x+12}}}{{\displaystyle \frac{2}{x-4}}}$

Simplify the complex rational expression by writing it as a division:

$\frac{{\displaystyle \frac{1}{2}}+{\displaystyle \frac{2}{3}}}{{\displaystyle \frac{5}{6}}+{\displaystyle \frac{1}{12}}}$

In the following exercises, add.

$\frac{2}{15}+\frac{7}{15}$

Simplify$\frac{2x^2-12xy+18y^2}{3x^2-27y^2}$.

Simplify the complex rational expression by writing it as division:

$\frac{{\displaystyle \frac{3}{4}}-{\displaystyle \frac{1}{3}}}{{\displaystyle \frac{1}{8}}+{\displaystyle \frac{5}{6}}}$

Simplify the complex rational expression by writing it as division:

$\frac{{\displaystyle \frac{1}{x}}+{\displaystyle \frac{1}{y}}}{{\displaystyle \frac{1}{x}}-{\displaystyle \frac{1}{y}}}$

$∆ABC$is similar to $∆XYZ$. The lengths of two sides of each triangle are given in the figure. Find the length of the third sides.