Solve the rational equation $\frac{2}{(x-3)} + \frac{1}{x} = \frac{(x-1)}{(x-3)}$.


Given: Equation $\frac{2}{(x-3)} + \frac{1}{x} = \frac{(x-1)}{(x-3)}$.

To do: To solve $\frac{2}{(x-3)} + \frac{1}{x} = \frac{(x-1)}{(x-3)}$.

Solution:

Given equation: $\frac{2}{(x-3)} + \frac{1}{x} = \frac{(x-1)}{(x-3)}$

$\Rightarrow \frac{2x+x-3}{x( x-3)}=\frac{(x-1)}{(x-3)}$

$\Rightarrow \frac{3x-3}{x}=x-1$

$\Rightarrow \frac{3( x-1)}{x}=( x-1)$

$\Rightarrow \frac{1}{x}=1$

$\Rightarrow x=1$

Thus, $x=1$.

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Updated on: 10-Oct-2022

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