# How do you add \frac{3x-2}{x-2}+\frac{1}{x^2-4x+4}?

Dec 11, 2014

$\frac{3 x - 2}{x - 2} + \frac{1}{{x}^{2} - 4 x + 4}$

by factoring out the denominator of the second quotient,

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

by multiplying the numerator and the denominator of the first quotient by $\left(x - 2\right)$,

$= \frac{3 {x}^{2} - 8 x + 4}{{\left(x - 2\right)}^{2}} + \frac{1}{{\left(x - 2\right)}^{2}}$

by combining the two quotients together,

$= \frac{3 {x}^{2} - 8 x + 5}{{\left(x - 2\right)}^{2}}$

by factoring out the numerator,

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

I hope that this was helpful.