SOLUTION: y/y-4 -6/y+7= y^2/y^2+3y-28

Question 136439This question is from textbook
: y/y-4 -6/y+7= y^2/y^2+3y-28 This question is from textbook

Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!

First off we need to find a common denominator. To do this I suggest factoring the denominator on the right hand side and seeing what you get.

y^2+3y-28
we need factors that add to 3 but multiply to -28
28:
1,28
2,14
-4,7

-4+7 = 3 and -4(7)=-28 so we know that
y^2+3y-28
=(y-4)(y+7)

Now that the denominator is factored it is very easy to see that our common denominator is going to be (y-4)(y+7) because every rational expression has either a y-4 or a y+7 in it. So multiply the top of the left hand side and right hand side by (y-4)(y+7) and solve the remaining equation.

--> Multiply by your common denominator.
--> cancel like terms
y(y+7)-6(y-4)= y^2 --> Distribute
y^2+7y-6y+24 = y^2 --> Collect Like Terms
y^2-y^2+7y-6y+24 = 0 --> Simplify
y+24 = 0 --> Subtract 24 from both sides(solve for y)
y = -24
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