SOLUTION: Add and simplify (if possible): (10/x^2+x-6)+(3x/x^2-4x+4)

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Question 1135: Add and simplify (if possible): (10/x^2+x-6)+(3x/x^2-4x+4)
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
By factoring x^2+x-6 = (x+3)(x-2)
and by squaring x^2-4x+4 = (x-2)^2
Wehave
10/(x^2+x-6)+ 3x/(x^2-4x+4)
= 10/[(x+3)(x-2)] + 3x/ (x-2)^2
= [10(x-2) + 3x (x+3)]/ [(x+3)(x-2)^2]
= (3x^2 + 19 x -20)/ [(x+3)(x-2)^2]