How do you simplify ((r+s)/(x^2-y^2))/((r+s)^2/(x-y))?

May 29, 2018

See Below.

Explanation:

We have,

((r + s)/(x^2 - y^2))/((r + s)^2/(x - y)) = ((r + s)/((x + y)(x - y)))/(((r + s)(r + s))/((x - y))

$= \frac{\cancel{\left(r + s\right)}}{\left(x + y\right) \cancel{\left(x - y\right)}} \times \frac{\cancel{\left(x - y\right)}}{\cancel{\left(r + s\right)} \left(r + s\right)}$ [As $\frac{a}{b} = a \times \frac{1}{b}$]

$= \frac{1}{\left(r + s\right) \left(x + y\right)}$

$= \frac{1}{r x + s x + r y + s y}$

Hope this helps.

May 29, 2018

$\frac{1}{\left(x + y\right) \left(r + s\right)}$

Explanation:

break it up like this:

$\frac{r + s}{{x}^{2} - {y}^{2}} \div {\left(r + s\right)}^{2} / \left(x - y\right)$

when dividing remember to keep the dividend, then change the division sign to a multiplication sign, and then use the reciprocal of the divisor.

$\frac{r + s}{{x}^{2} - {y}^{2}} \cdot \frac{x - y}{r + s} ^ 2$

you can simplify the expression further. You can factor ${x}^{2} - {y}^{2}$ to $\left(x + y\right) \left(x - y\right)$

$\frac{r + s}{\left(x + y\right) \left(x - y\right)} \cdot \frac{x - y}{\left(r + s\right) \left(r + s\right)}$

now just multiply the two of these like you would do for normal fractions

$\frac{\cancel{\left(r + s\right)} \cancel{\left(x - y\right)}}{\left(x + y\right) \cancel{\left(x - y\right)} \cancel{\left(r + s\right)} \left(r + s\right)}$

some of the terms are going to cancel each other out leaving you with this answer
$\frac{1}{\left(x + y\right) \left(r + s\right)}$