SOLUTION: simplify or perform operation: 215) 2x – 5 / (x – 2)(x + 6) + x2 – 2x + 1 / (x – 2)(x + 6) 217.) 2/(x-3) + 3/(3-x)

Algebra ->  Expressions-with-variables -> SOLUTION: simplify or perform operation: 215) 2x – 5 / (x – 2)(x + 6) + x2 – 2x + 1 / (x – 2)(x + 6) 217.) 2/(x-3) + 3/(3-x)      Log On


   

Question 178161: simplify or perform operation:
215) 2x – 5 / (x – 2)(x + 6) + x2 – 2x + 1 / (x – 2)(x + 6)
217.) 2/(x-3) + 3/(3-x)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
215) [(2x – 5) / (x – 2)(x + 6)] + [(x^2 – 2x + 1) / (x – 2)(x + 6)]
[(2x – 5) / (x – 2)(x + 6)] + [(x^2 – 1)^2 / (x – 2)(x + 6)]
The denominators are the same so combine the numerators to get:
= [2x - 5 + x^2 -2x + 1] / [(x-2)(x+6)]
= [x^2-4] / [(x-2)(x+6)]
= (x+2)/(x+6)
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217.) 2/(x-3) + 3/(3-x)
Modify to get:
2(x-3) - 3 (x-3)
= (2-3)/(x-3
= -1/(x-3)
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Cheers,
Stan H.