How do you add \frac{3x-2}{x-2}+\frac{1}{x^2-4x+4}3x2x2+1x24x+4?

1 Answer
Dec 11, 2014

{3x-2}/{x-2}+1/{x^2-4x+4}3x2x2+1x24x+4

by factoring out the denominator of the second quotient,

={3x-2}/{x-2}+1/{(x-2)^2}=3x2x2+1(x2)2

by multiplying the numerator and the denominator of the first quotient by (x-2)(x2),

={3x^2-8x+4}/{(x-2)^2}+1/{(x-2)^2}=3x28x+4(x2)2+1(x2)2

by combining the two quotients together,

={3x^2-8x+5}/{(x-2)^2}=3x28x+5(x2)2

by factoring out the numerator,

={(3x-5)(x-1)}/{(x-2)^2}=(3x5)(x1)(x2)2


I hope that this was helpful.