SOLUTION: Please help me help my daughter with rational expressions. x+1 over (x+3)(x-3)plus 4(x-3) over (x+3)(x-3)plus (x-1)(x-3) over (3-x)(x+3) =? Also, 6 over x-y plus 4x ov

Click here to see ALL problems on expressions

Question 78602: Please help me help my daughter with rational expressions.
x+1 over (x+3)(x-3)plus 4(x-3) over (x+3)(x-3)plus (x-1)(x-3) over (3-x)(x+3) =?

Also,
6 over x-y plus 4x over y^2 - x^2 =?

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
(x+1)/(x+3)(x-3) + 4(x-3) / (x+3)(x-3) + (x-1)(x-3) / (3-x)(x+3)
Adjust the 3rd term so it has the same denominator as the 1st and 2nd terms.
----------
=(x+1)/(x+3)(x-3) + 4(x-3) / (x+3)(x-3) - (x-1)(x-3) / (x-3)(x+3)
Combine the numerators over a single denominator, as follows:
=[x+1+4x-12-x^2+4x-3]/[(x-3)(x+3)]
=[-(x^2-9x+2]/[(x-3)(x+3)]
================================

Also,
6 /(x-y) + 4x/(y^2 - x^2)
=6 /(x-y) - 4x/(x^2 - y^2)
The least common denominator is (x-y)(x+y)
=6(x+y)/lcm - 4x/lcm
=[6x+6y-4x]/lcm
=[2x+6y]/[(x-y)(x+y)]
---------
Cheers,
Stan H.