How do you combine #3/(x+2) - 2/(x^2+x-2) + 2/(x-1)#?

1 Answer
Guilherme N.
May 25, 2015

You need to find the lowest common denominator between these fractions. To simplify things for us, we can factor the second fraction's denominator:

#(-1+-sqrt(1-4(1)(-2)))/2=(-1+-3)/2#
#x_1=1#, thus being the factor #(x-1)=0#
#x_2=-2#, thus being the factor #(x+2)=0#

Rewriting everything, we have that the l.c.d. is #(x-1)(x+2)#.

#3/(x+2)-2/((x-1)(x+2))+2/(x-1)#

#(3(x-1)-2+2(x+2))/((x-1)(x+2))#=#(3x-3-2+2x+4)/((x-1)(x+2))#=#(5x-1)/(x^2+x-2)#

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