# How do you solve 2/x + 1/(x+1) = 5/(x^2+x)?

Jun 4, 2015

You may have noticed, that ${x}^{2} + x = x \cdot \left(x + 1\right)$

So we may multiply every part of the equation by $x \cdot \left(x + 1\right)$ and get rid of all the denominators.
BUT: $x \ne 0 \mathmr{and} x \ne - 1$ or one of the denominators $= 0$

The equation goes into:
$\to 2 \cdot \left(x + 1\right) + x = 5 \to 3 x = 3 \to$$x = 1$
And this is allowed.

$\frac{2}{1} + \frac{1}{1 + 1} = \frac{5}{{1}^{2} + 1} = 2 \frac{1}{2}$