Question

What is the solution to the equation StartFraction y Over y minus 4 EndFraction minus StartFraction 4 Over y + 4 EndFraction = StartFraction 32 Over y squared minus 16 EndFraction?

Answer 1

Answer:

Step-by-step explanation:

Given:

(y/y - 4) - (4/y + 4) = 32/y^2 - 16

Note y^2 - 16 = (y - 4 ) × (y + 4)

Multiplying the equation; both sides by y^2 - 16,

y (y + 4) - (4(y - 4)) = 32

y^2 + 4y - 4y + 16 = 32

y^2 = 32 - 16

Squaring both sides,

y = sqrt(16)

= 4

Answer 2

The solution to the given equation is 4 and -4

Given the function:

$\frac{y}{y-4} -\frac{4}{y+4}=\frac{32}{y^2-16}$

Find the least common denominator of the function:

$=\frac{y}{y-4} -\frac{4}{y+4}\\=\frac{y(y+4)-4(y-4)}{(y-4)(y+4)} \\=\frac{y^2+4y-4y+16}{(y-4)(y+4)}\\=\frac{y^2+16}{y^2-16}$

Equating the result to $\frac{32}{y^2-16}$

$\frac{y^2+16}{y^2-16} = \frac{32}{y^2-16}\\y^2 + 16 = 32\\y^2= 32-16\\y^2=16\\y = \pm \sqrt{16} \\y= \pm 4$

Hence the solution to the given equation is 4 and -4

Learn more on sum of functions here; https://brainly.com/question/17431959