Question

1/p+q+x=1/p+1/q+1/x solve for x by factorization method

Answer 1

Given $\frac{1}{p}+\frac{1}{q}+\frac{1}{x}=\frac{1}{p+q+x}$

$\implies\bold{\frac{1}{p}+\frac{1}{q}=\frac{1}{p+q+x}-\frac{1}{x}}$

$\implies\bold{\frac{q+p}{pq}=\frac{x-(p+q+x)}{x(p+q+x)}}$

$\implies\bold{\frac{p+q}{pq}=\frac{-(p+q)}{x(p+q+x)}}$

$\implies\bold{\frac{1}{pq}=\frac{-1}{x(p+q+x)} (Since,\:p+q \not= 0)}$

$\implies\bold{x(p+q+x)=-pq}$

$\implies\bold{px+qx+x^2+pq=0}$

$\implies\bold{x^2+px+qx+pq=0}$

$\implies\bold{x ( x + p ) + q ( x + p ) = 0}$

$\implies\bold{( x + p ) . ( x + q ) = 0}$

$\boxed{\bold{\therefore(x + p = 0)\:\: OR \:\:(x + q = 0)}}$