How do you simplify the expression #x/(x+1) + 3/(x-1)#?

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Answer 1 · 2015-04-09T23:15:18

First you should make the denominators same;

# x/(x+1) + 3/(x-1)#
so i will multiply the first term with #(x-1)/(x-1)#
and the second term with #(x+1)/(x+1)#;

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

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

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

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

I can only get this far. I don't know if there is a more simplest result. I hope it helps.