Solve the equation by factorisation: ${\left(a+b\right)}^2{x}^2-4abx-{\left(a-b\right)}^2=0$.

Solve the equation by factorisation: $ab{x}^2+\left(b^2-ac\right)x-bc=0$.

Solve the equation by factorisation: $a^2{b}^2{x}^2+b^{2}x-a^{2}x-1=0$.

Solve the equation by factorisation: $\frac{1}{x-1}-\frac{1}{x+5}=\frac{6}{7}, x\ne 1, -5$

Solve the equation by factorisation:

$\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}, x\ne -3, 5$.

Solve the equation by factorisation:

$2\left(\frac{x-1}{x+3}\right)-7\left(\frac{x+3}{x-1}\right)=5, x\ne -3, 1$.

Solve the equation by factorisation:

$\frac{a}{ax-1}+\frac{b}{bx-1}=a+b, x\ne \frac{1}{a}+\frac{1}{b}$.

Solve the equation by factorisation:

$\frac{3}{x+1}-\frac{1}{2}=\frac{2}{3x-1}, x\ne 1, \frac{1}{3}$.

Solve the equation by factorisation:

$\frac{x-4}{x-5}-\frac{x-6}{x-7}=\frac{10}{3}, x\ne 5, 7$.

Note: The question given in the textbook seems to be wrong. The correct question should be as below:

Solve the equation by factorisation:

$\frac{x-4}{x-5}+\frac{x-6}{x-7}=\frac{10}{3}, x\ne 5, 7$.