Question

Hallar x en la ecuacion

Answer 1

Respuesta:

x = q - p

Explicación paso a paso:

$\displaystyle \frac{x+p}{q}-1=\frac{x-q}{p}+1 \\\\\\ \frac{x+p}{q}pq-1\cdot pq=\frac{x-q}{p}pq+1\cdot pq \\\\\\ p(x+p)-pq=q(x-q)+pq \\\\\\ xp+p^2-pq=q(x-q)+pq \\\\\\ xp+p^2-pq=xq-q^2+pq \\\\\\ xp+p^2-pq-(p^2-pq)=xq-q^2+pq-(p^2-pq) \\\\\\ xp=-q^2+xq+2pq-p^2 \\\\\\ xp-xq=-q^2+xq+2pq-p^2-xq \\\\\\ xp-xq=-q^2+2pq-p^2 \\\\\\ x(p-q)=-q^2+2pq-p^2 \\\\\\ \frac{x(p-q)}{p-q}=-\frac{q^2}{p-q}+\frac{2pq}{p-q}-\frac{p^2}{p-q} \\\\\\ \boxed{\mathsf{x=q-p}}$

Espero te ayude.