SOLUTION: Will somrone please help me solve this problem? perform the indicated operation and simplify:5x/x-1-x/x+2+6/x^2+x-2

Question 111037: Will somrone please help me solve this problem? perform the indicated operation and simplify:5x/x-1-x/x+2+6/x^2+x-2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
5x/(x-1)-x/(x+2)+6/(x^2+x-2)
LCD = (x-1)(x+2)
Rewrite each fraction with the LCD as its denominator:
= [5x(x+2)/LCD] -[x(x-1)/LCD] + [6/LCD]
All the denominators are the same so combine the numerators over the LCD:

= [5x^2+10x-x^2+x+6]/LCD
= [4x^2+11x+6]/LCD
= [4x^2+8x+3x+6]/LCD
= [4x(x+2)+3(x+2)]/LCD
= [(x+2)(4x+3)]/[(x-1)(x+2)]
= (4x+3)/(x-1)
==================
Cheers,
Stan H.
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