SOLUTION: Find the value of Y 30. 6 + 1/y + 1 = 6/y + 3

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Question 171821: Find the value of Y
30. 6 + 1/y + 1 = 6/y + 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6%2B%281%29%2F%28y%2B1%29=%286%29%2F%28y%2B3%29 Start with the given equation.


Multiply EVERY term on both sides by the LCD %28y%2B1%29%28y%2B3%29. Doing this will eliminate all of the fractions.


6%28y%2B1%29%28y%2B3%29%2B1%28y%2B3%29=6%28y%2B1%29 Simplify


6%28y%5E2%2B4y%2B3%29%2B1%28y%2B3%29=6%28y%2B1%29 FOIL


6y%5E2%2B24y%2B18%2By%2B3=6y%2B6 Distribute


6y%5E2%2B24y%2B18%2By%2B3-6y-6=0 Subtract 6y from both sides. Subtract 6 from both sides.


6y%5E2%2B19y%2B15=0 Combine like terms.


Notice we have a quadratic equation in the form of ay%5E2%2Bby%2Bc where a=6, b=19, and c=15


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-%2819%29+%2B-+sqrt%28+%2819%29%5E2-4%286%29%2815%29+%29%29%2F%282%286%29%29 Plug in a=6, b=19, and c=15


y+=+%28-19+%2B-+sqrt%28+361-4%286%29%2815%29+%29%29%2F%282%286%29%29 Square 19 to get 361.


y+=+%28-19+%2B-+sqrt%28+361-360+%29%29%2F%282%286%29%29 Multiply 4%286%29%2815%29 to get 360


y+=+%28-19+%2B-+sqrt%28+1+%29%29%2F%282%286%29%29 Subtract 360 from 361 to get 1


y+=+%28-19+%2B-+sqrt%28+1+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


y+=+%28-19+%2B-+1%29%2F%2812%29 Take the square root of 1 to get 1.


y+=+%28-19+%2B+1%29%2F%2812%29 or y+=+%28-19+-+1%29%2F%2812%29 Break up the expression.


y+=+%28-18%29%2F%2812%29 or y+=++%28-20%29%2F%2812%29 Combine like terms.


y+=+-3%2F2 or y+=+-5%2F3 Simplify.


So the answers are y+=+-3%2F2 or y+=+-5%2F3