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

banganX 2021-08-17 Answered
Solve this equation \(\displaystyle\frac{{{2}{x}}}{{{x}+{2}}}={x}–{1}\)

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Expert Answer

Brighton
Answered 2021-08-18 Author has 18209 answers
\(\displaystyle\frac{{{2}{x}}}{{{x}+{2}}}={x}–{1}\)
\(\displaystyle\frac{{{2}{x}}}{{{x}+{2}}}\times{\left({x}+{2}\right)}={\left({x}–{1}\right)}{\left({x}+{2}\right)}\)
\(\displaystyle{2}{x}={\left({x}–{1}\right)}{\left({x}+{2}\right)}\)
\(\displaystyle{2}{x}={x}^{{2}}–{x}+{2}{x}–{2}–{2}{x}\)
\(\displaystyle{x}^{{2}}–{x}+{2}{x}–{2}–{2}{x}=\)
\(\displaystyle{x}^{{2}}–{x}–{2}={0}\)
\(\displaystyle{x}^{{2}}–{2}{x}+{x}–{2}={0}\)
\(\displaystyle{\left({x}+{1}\right)}{\left({x}–{2}\right)}={0}\)
Thus, x = -1. x = 2.
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