# How do you solve (40/(x-2))=1+(42/(x- 2))?

Jun 13, 2016

$x = 0$

#### Explanation:

Given,

$\frac{40}{x - 2} = 1 + \frac{42}{x - 2}$

Multiply each term on the left and right sides by $x - 2$ to get rid of the denominators.

$\textcolor{red}{\left(x - 2\right)} \left(\frac{40}{x - 2}\right) = 1 \textcolor{red}{\left(x - 2\right)} + \textcolor{red}{\left(x - 2\right)} \left(\frac{42}{x - 2}\right)$

Simplify.

$\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{x - 2}}}\right) \left(\frac{40}{\textcolor{red}{\cancel{\textcolor{b l a c k}{x - 2}}}}\right) = 1 \left(x - 2\right) + \left(\textcolor{red}{\cancel{\textcolor{b l a c k}{x - 2}}}\right) \left(\frac{42}{\textcolor{red}{\cancel{\textcolor{b l a c k}{x - 2}}}}\right)$

$40 = x - 2 + 42$

$40 = x + 40$

Subtract $40$ from both sides.

$40 \textcolor{w h i t e}{i} \textcolor{red}{- 40} = x + 40 \textcolor{w h i t e}{i} \textcolor{red}{- 40}$

$x = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{0} \textcolor{w h i t e}{\frac{a}{a}} |}}}$