Question

1/p+q+x= 1/p+1/q+1/x solve for x

Answer 1

Answer :

Now,

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

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

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

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

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

$\implies \frac{-1}{x(p+q+x)} = \frac{1}{pq}$

➩ -x(p+q+x) = pq

➩-px - qx - x² = pq

➩ x² + px + qx + pq = 0

➩ x (x + p) + q (x + p) = 0

➩ (x + p) (x + q) = 0

Either x + p = 0 or, x + q = 0

➩ x = - p, x = - q

Therefore, the required solution be

x = - p, - q

#MarkAsBrainliest