# How do you solve the equation and identify any extraneous solutions for 1/(x-1) + 4/(4x-4) = 2?

Jun 11, 2015

Extraneous would be if one of the numerator would be $= 0$
In both fractions that means $x \ne 1$

#### Explanation:

We can divide top and bottom of the second fraction by $4$:
$\frac{1}{x - 1} + \frac{1}{x - 1} = \frac{2}{x - 1} = 2 \to$

$\frac{1}{x - 1} = 1 \to x - 1 = 1 \to x = 2$

And this is allowed.