How do you evaluate #\frac { 3} { x + 1} + \frac { 2x - 5} { x ^ { 2} - 3x - 4}#?

1 Answer
maganbhai P.
Mar 7, 2018

#(5x-17)/((x+1)(x-4))#

Explanation:

We have,#x^2-3x-4=x^2-4x+x-4=x(x-4)+1(x-4)=(x+1)(x-4)#
So,
#3/(x+1)+(2x-5)/(x^2-3x-4)=3/(x+1)+(2x-5)/((x+1)(x-4))#
#=(3(x-4))/((x+1)(x-4))+(2x-5)/((x+1)(x-4))#
#=(3(x-4)+2x-5)/((x+1)(x-4))=(3x-12+2x-5)/((x+1)(x-4))=(5x-17)/((x+1)(x-4))=(5x-17)/(x^2-3x-4)#

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