SOLUTION: Find all values of y satisfying the equation. -_7___ _3__ y + 1 = -4 - y-4 Both have minuses before the fractions and the last one has a -4 before it as well. H

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Question 225144: Find all values of y satisfying the equation.
-_7___ _3__
y + 1 = -4 - y-4
Both have minuses before the fractions and the last one has a -4 before it as well. Help.
(If there is more than one solution, separate them with commas.)
Answer by ankor@dixie-net.com(12704) About Me  (Show Source):
You can put this solution on YOUR website!
-_7___ _3__
y + 1 = -4 - y-4
Assume it's
-7%2F%28y%2B1%29 = -4 - 3%2F%28y-4%29
Multiply by (y+1)(y-4)*
(y+1)(y-4)*-7%2F%28y%2B1%29 = -4(y+1)(y-4) - (y+1)(y-4)*3%2F%28y-4%29
:
cancel the denominators and you have
-7(y-4) = -4(y+1)(y-4) - 3(y+1)
:
-7y + 28 = -4(y^2 - 4y + y - 4) - 3y - 3
:
-7y + 28 = -4(y^2 - 3y - 4) - 3y - 3
:
-7y + 28 = -4y^2 + 12y + 16 - 3y - 3
:
-7y + 28 = -4y^2 + 9y + 13
:
4y^2 - 7y - 9y + 28 - 13 = 0
:
4y^2 - 16y + 15 = 0
Factor this to
(2x - 5)(2x - 3) = 0
Two solutions
2x = 5
x = 2.5
and
2x = 3
x = 1.5
:
x = 2.5, 1.5
:
:
Check solution using x=2.5
-7%2F%282.5%2B1%29 = -4 - 3%2F%282.5-4%29
-7%2F%283.5%29 = -4 - 3%2F%28-1.5%29
-2 = -4 + 2
:
you can check it using the x=1.5 solution