(y/(y^2-16)-(2/(y^2+9y+20))=1/(y-4)

UkusakazaL

UkusakazaL

Answered question

2021-01-30

(yy216(2y2+9y+20)=1y4

Answer & Explanation

gotovub

gotovub

Skilled2021-01-31Added 98 answers

We are given the equation: (y(y2)16(2y+5(y+4))=1y4
Here, we note that y=-4,4,-5 are not solutions.
We multiply both sides by the LCD which is (y-4)(y+4)(y+5):
[(y(y4)(y+4)(2y+5(y+4)))](y4)(y+4)(y+5)=(1y4)(y4)(y+4)(y+5)
y(y+5)-2(y-4)=(y+4)(y+5)
y2+5y2y+8=y2+9y+20
3y+8=9y+20
3y=9y-12
-6y=-12
y=-2

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