Question

I really could use some help.

Simplify x-(y/(x/y)+(y/x))

Answer 1

$$
x-(y/(x/y)+(y/x))
$$
Is this the problem?

Answer 2

$$
\Large{
x- \cfrac{y}{{x \over y} + {y \over x}}\\
=x- \cfrac{y}{{x^2 \over xy} + {y^2 \over xy}}\\
=x- \cfrac{y}{{x^2 \over xy} + {y^2 \over xy}}\\
=x- \cfrac{y}{{x^2 + y^2 \over xy} }\\
=x- \cfrac{xy^2}{x^2 + y^2 }\\
=\cfrac{x(x^2 + y^2) - xy^2}{x^2 + y^2}\\
=\cfrac{x^4 + xy^2 - xy^2}{x^2 + y^2}\\
=\cfrac{x^4 }{x^2 + y^2}\\
}
$$

Make sense?

Answer 3

Honestly, I'm not sure if it is my computer but the entire thing looks like html

Answer 4

How's that?

Answer 5

I was keeping up until step 4-5, I got lost there

Answer 6

So I multiplied the numerator and denominator by xy to eliminate xy at the bottom:

When I did this, I multiply y times xy to get xy^2. And when I multiplied it at the bottom, it eliminated xy in the lower denominator:

y/ (x^2 + y^2) / xy = xy y / (x^2 +y^2) = xy^2 / (x^2 + y^2)

Answer 7

Okay, that is a lot clearer now. Thank you very much.

Answer 8

NP