# How do you solve (3x)/(x-2)=(3x+5)/(x-1) and find any extraneous solutions?

Jun 7, 2017

$x = \textcolor{red}{5}$

#### Explanation:

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

We'll use cross multiplication to simplify the equation:

$3 x \left(x - 1\right) = \left(x - 2\right) \left(3 x + 5\right)$

We'll then use the distributive property on both sides of the equation to make things easier:

$\left(3 x\right) \left(x\right) - \left(3 x\right) \left(1\right) = \left(x - 2\right) \left(3 x\right) + \left(x - 2\right) \left(5\right)$
$3 {x}^{2} - 3 x = 3 {x}^{2} - 6 x + 5 x - 10$

Now, we combine like terms:

$3 {x}^{2} - 3 x = 3 {x}^{2} - 6 x + 5 x - 10$
$- 3 x = - 6 x + 5 x - 10$
$- 2 x = - 10$
$x = \frac{- 10}{-} 2 = \textcolor{red}{5}$