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What is the solution to the equation y/y-4 -4/y+4=32/y2-16?

What is the solution to the equation y/y-4 -4/y+4=32/y2-16?-example-1
User Hypnotic
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1 Answer

8 votes
8 votes

Answer:

No solution

Explanation:

For the equation given, we have an alternate form that is


(y^2 + 16)/(y^2-16) =(32)/(y^2-16)

It is clear that


y^2+16 = 32 \implies y=4, y=-4

But the denominator goes to zero and it is undefined.

If you take


$\lim _(y\to 4)\left((y^2+16)/(y^2-16)\right)$

you'll see that


$\lim _(y\to 4^-)\left((y^2+16)/(y^2-16)\right) = -\infty$


$\lim _(y\to 4^+)\left((y^2+16)/(y^2-16)\right) =\infty$

It diverges and the limit does not exist.

User Abel Osorio
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