SOLUTION: 8-(5/y+2)=1/y+1

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Question 180894: 8-(5/y+2)=1/y+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
8-5%2F%28y%2B2%29=1%2F%28y%2B1%29 Start with the given equation.


Multiply EVERY term by the LCD %28y%2B2%29%28y%2B1%29 to clear out the fractions.


8%28y%2B2%29%28y%2B1%29-5%28y%2B1%29=1%28y%2B2%29 Multiply and simplify


8%28y%5E2%2B3y%2B2%29-5%28y%2B1%29=1%28y%2B2%29 FOIL


8y%5E2%2B24y%2B16-5y-5=y%2B2 Distribute


8y%5E2%2B24y%2B16-5y-5-y-2=0 Subtract y from both sides. Subtract 2 from both sides.

8y%5E2%2B18y%2B9=0 Combine like terms.


Notice we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=8, b=18, and c=9


Let's use the quadratic formula to solve for y


y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


y+=+%28-%2818%29+%2B-+sqrt%28+%2818%29%5E2-4%288%29%289%29+%29%29%2F%282%288%29%29 Plug in a=8, b=18, and c=9


y+=+%28-18+%2B-+sqrt%28+324-4%288%29%289%29+%29%29%2F%282%288%29%29 Square 18 to get 324.


y+=+%28-18+%2B-+sqrt%28+324-288+%29%29%2F%282%288%29%29 Multiply 4%288%29%289%29 to get 288


y+=+%28-18+%2B-+sqrt%28+36+%29%29%2F%282%288%29%29 Subtract 288 from 324 to get 36


y+=+%28-18+%2B-+sqrt%28+36+%29%29%2F%2816%29 Multiply 2 and 8 to get 16.


y+=+%28-18+%2B-+6%29%2F%2816%29 Take the square root of 36 to get 6.


y+=+%28-18+%2B+6%29%2F%2816%29 or y+=+%28-18+-+6%29%2F%2816%29 Break up the expression.


y+=+%28-12%29%2F%2816%29 or y+=++%28-24%29%2F%2816%29 Combine like terms.


y+=+-3%2F4 or y+=+-3%2F2 Simplify.


So the answers are y+=+-3%2F4 or y+=+-3%2F2