Eliminando a variável do denominador

[Miola]

\(x(\frac{1}{x}+\frac{1}{x+5})\)

Resposta: \(\frac{x}{6}\)

[danjr5]

Olá!

\(x \cdot \left ( \frac{1}{x} + \frac{1}{x + 5} \right ) =\)

\(x \cdot \left ( \frac{1}{x/(x + 5)} + \frac{1}{x + 5/x} \right ) =\)

\(x \cdot \left ( \frac{1 \cdot (x + 5) + 1 \cdot x}{x(x + 5)} \right ) =\)

\(x \cdot \left ( \frac{x + 5 + x}{x(x + 5)} \right ) =\)

\(\frac{x(2x + 5)}{x(x + 5)} =\)

\(\fbox{\frac{2x + 5}{x + 5}}\)