# How do you solve (3x)/(x+9)+1=x/(x+9) and check for extraneous solutions?

Nov 23, 2016

$x = - 3$

#### Explanation:

$\frac{3 x}{x + 9} + 1 = \frac{x}{x + 9}$

Subtract $\frac{x}{x + 9}$ from both sides.

$\frac{3 x}{x + 9} - \frac{x}{x + 9} + 1 = 0$

Subtract $1$ from both sides.

$\frac{3 x}{x + 9} - \frac{x}{x + 9} = - 1$

Combine the two terms on the left.

$\frac{3 x - x}{x + 9} = - 1$

$\frac{2 x}{x + 9} = - 1$

Multiply both sides by $\left(x + 9\right)$.

$2 x = - 1 \left(x + 9\right)$

$2 x = - x - 9$

Add $x$ to both sides.

$3 x = - 9$

Divide both sides by $3$.

$x = - 3$