Question

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

Answer 1

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.