Question 111037
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)
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Cheers,
Stan H.