# How do you solve 3/(x-3)-4=x/(x-3) and check for extraneous solutions?

Apr 7, 2018

$x = 3$ is extraneous solution, so original equation has no solution.

#### Explanation:

 3/(x-3)-4=x/(x-3); x!=3 . Multiplying by $\left(x - 3\right)$ on both

sides we get, $3 - 4 \left(x - 3\right) = x \mathmr{and} 3 - 4 x + 12 = x$ or

$5 x = 15 \mathmr{and} x = 3$ Check : $\frac{3}{3 - 3} - 4 = \frac{x}{3 - 3}$

$f \left(x\right)$ is undefined at $x = 3$ Therefore, it cannot be a root of the

original equation. $x = 3$ extraneous solution, so original equation

has no solution. [Ans]