Solve the following equation and find $x$.

$\frac{\left(x+1\right)\left(x+2\right)}{\left(x+11\right)\left(x-2\right)}=1$

Solve the following equation and find $x$.

$\frac{{\displaystyle \frac{x}{4}-\frac{3}{5}}}{{\displaystyle \frac{4}{3}-7x}}=\frac{-3}{20}$

Solve the following equation to find the value of $x$.

$\frac{{\displaystyle \frac{3}{4}x+7}}{{\displaystyle \frac{2}{5}x-4}}=\frac{5}{4}$

Find the value of $-7x$.

$\frac{8x+3}{2\left(x-2\right)}=\frac{4x}{x-5}$

Solve the following equation and write down the value of $7x$.

$\frac{4x-5}{x+2}=\frac{8x-1}{2x+1}$

Solve the following equation and find $x$.

$\frac{x+a}{x-a}=\frac{b-a}{b+a}$