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

Just use this formula V= 1/2 bxhxl...

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

gabbypittman20

25.04.2021

No solution

Step-by-step explanation:

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

$\dfrac{y^2 + 16}{y^2-16} =\dfrac{32}{y^2-16}$

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

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

you'll see that

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

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

It diverges and the limit does not exist.

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