SOLUTION: simplify {{{(y+1)/(y^2-4) - 5/(y+2)}}}

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: simplify {{{(y+1)/(y^2-4) - 5/(y+2)}}}      Log On


   

Question 1140824: simplify %28y%2B1%29%2F%28y%5E2-4%29+-+5%2F%28y%2B2%29
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%28y%2B1%29%2F%28y%5E2-4%29+-+5%2F%28y%2B2%29
---
y%5E2-4+=+%28y-2%29%2A%28y%2B2%29
======================
%28y%2B1%29%2F%28%28y-2%29%2A%28y%2B2%29%29+-+5%2F%28y%2B2%29
= %28y%2B1%29%2F%28%28y-2%29%2A%28y%2B2%29%29+-+5%28y-2%29%2F%28%28y-2%29%2A%28y%2B2%29%29
= %28y%2B1%29%2F%28%28y-2%29%2A%28y%2B2%29%29+-+%285y-10%29%2F%28%28y-2%29%2A%28y%2B2%29%29
= %28-4y%2B11%29%2F%28%28y-2%29%2A%28y%2B2%29%29
= %28-4y%2B11%29%2F%28y%5E2-4%29

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
simplify %28y%2B1%29%2F%28y%5E2-4%29+-+5%2F%28y%2B2%29
factor the 1st denominator
%28y%2B1%29%2F%28%28y-2%29%28y%2B2%29%29+-+5%2F%28y%2B2%29
over a single common denominator
%28%28y%2B1%29-5%28y-2%29%29%2F%28%28y-2%29%28y%2B2%29%29
distribute the -5
%28%28y%2B1-5y%2B10%29%29%2F%28%28y-2%29%28y%2B2%29%29
combine like terms
%28%28-4y%2B11%29%29%2F%28%28y-2%29%28y%2B2%29%29 or %28%28-4y%2B11%29%29%2F%28%28y%5E2-4%29%29