# How do you solve 2 + (3/(x-1)) = 10?

Mar 10, 2016

You must start by putting on an equal denominator.

#### Explanation:

The LCD (least common denominator) is $x - 1$

$\frac{2 \left(x - 1\right)}{x - 1} + \frac{3}{x - 1} = \frac{10 \left(x - 1\right)}{x - 1}$

We can now eliminate the denominators and solve.

$2 x - 2 + 3 = 10 x - 10$

$11 = 8 x$

$\frac{11}{8} = x$

Practice exercises:

1. Solve for x.

$\frac{2}{2 x + 3} + \frac{3}{x - 1} = \frac{5}{x - 1}$

Challenge problem:

Solve for x: $\frac{1}{x} + \frac{1}{x y} = \frac{2}{y + x}$

Good luck!