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

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Answer 1 · 2014-12-11T06:38:03

#{3x-2}/{x-2}+1/{x^2-4x+4}#

by factoring out the denominator of the second quotient,

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

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

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

by combining the two quotients together,

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

by factoring out the numerator,

#={(3x-5)(x-1)}/{(x-2)^2}#

I hope that this was helpful.