# Solve this equation (2x)/(x + 2) = x – 1

Solve this equation $$\displaystyle\frac{{{2}{x}}}{{{x}+{2}}}={x}–{1}$$

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Brighton
$$\displaystyle\frac{{{2}{x}}}{{{x}+{2}}}={x}–{1}$$
$$\displaystyle\frac{{{2}{x}}}{{{x}+{2}}}\times{\left({x}+{2}\right)}={\left({x}–{1}\right)}{\left({x}+{2}\right)}$$
$$\displaystyle{2}{x}={\left({x}–{1}\right)}{\left({x}+{2}\right)}$$
$$\displaystyle{2}{x}={x}^{{2}}–{x}+{2}{x}–{2}–{2}{x}$$
$$\displaystyle{x}^{{2}}–{x}+{2}{x}–{2}–{2}{x}=$$
$$\displaystyle{x}^{{2}}–{x}–{2}={0}$$
$$\displaystyle{x}^{{2}}–{2}{x}+{x}–{2}={0}$$
$$\displaystyle{\left({x}+{1}\right)}{\left({x}–{2}\right)}={0}$$
Thus, x = -1. x = 2.