# How do you solve (u-2)/(u-3) + 3= u + (u-4)/(3-u) and find any extraneous solutions?

Jul 26, 2017

$\frac{u - 2}{u - 3} + 3 = u + \frac{u - 4}{3 - u}$

$\frac{u - 2}{u - 3} + 3 = u - \frac{u - 4}{u - 3}$

$\frac{u - 2}{u - 3} + \frac{u - 4}{u - 3} = u - 3$

$\frac{2 u - 6}{u - 3} = u - 3$

$u - 3 = 2 \cdot \frac{u - 3}{u - 3}$

$u - 3 = 2$

$u = 5$

#### Explanation:

1) I rewrote polynomial.

2) I left polynomials to left side and polynomials to right one.

3) I simplified polynomial due to x isn't equal to 3 condition.

4) I solved equation.