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Y+1 y+8 y+2 y+7

----- + ----- = ----- + -----
y+2 y+9 y+3 y+8

find y
plssssss help this is fraction

User Zeng Cheng
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1 Answer

4 votes


(y+1)/(y+2)+(y+8)/(y+9)=(y+2)/(y+3)+(y+7)/(y+8)

Write all fractions in terms of a common denominator:


(y+1)/(y+2)=((y+1)(y+9)(y+3)(y+8))/((y+2)(y+9)(y+3)(y+8))


(y+8)/(y+9)=((y+8)^2(y+2)(y+3))/((y+2)(y+9)(y+3)(y+8))


(y+2)/(y+3)=((y+2)^2(y+9)(y+8))/((y+2)(y+9)(y+3)(y+8))


(y+7)/(y+8)=((y+7)(y+2)(y+9)(y+3))/((y+2)(y+9)(y+3)(y+8))

Then move all fractions to one side and simplify the numerator:


((y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3))/((y+2)(y+9)(y+3)(y+8))=0

The numerator dictates when the fraction reduces to 0. The denominator can never be 0, so we know that y cannot take any of the values -2, -9, -3, nor -8.

So the equation reduces to


(y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)=0

Expand the left side; you would end up with


-6(2y+11)=0


2y+11=0


2y=-11


\implies\boxed{y=-\frac{11}2}

User Trincot
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