Question

Z^2-y^2/a^2-b^2 divided by z+y/a-b

Answer 1

Hello!

The answer is:

$\frac{z-y}{a+b}$

Why?

We need to simplify the fractions in order to find the answer.

Also, we must remember that:

$a^{2}-b^{2}=(a+b)(a-b)$

So, simplificating the first fraction, we have:

$\frac{z^{2} -y^{2}}{a^{2}-b^{2}}=\frac{(z+y)(z-y)}{(a+b)(a-b)}$

Then, let's divide each fraction:

To divide fractions, we need to multiply the first equation (numerator) by the reciprocal of the the second fraction (denominator).

The reciprocal of the second fraction, for this case, the denominator, is:

$\frac{a-b}{z+y}$

Hence,

$\frac{(z+y)(z-y)}{(a+b)(a-b)}*\frac{a-b}{z+y}=\frac{z-y}{a+b}$

So, the final fraction is:

$\frac{z-y}{a+b}$

Have a nice day!