# what algebraic manipulation was used here?

#### Evin

I have the equation $$\displaystyle (y-x*y/x)/y^2 = (y^2−x^2)/y^3$$

in my understanding the answer should be $$\displaystyle (y-x^2)/y^3$$. I just can't figure out what was done to get the first y squared.

Edit: forgot to add ^ before powers

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#### romsek

Math Team

$$\displaystyle \dfrac{y-x \cdot \dfrac{y}{x}}{y^2} = 0$$

The $x$'s cancel out leaving $y-y$ in the numerator.

$$\displaystyle \dfrac{y-x \cdot \dfrac{x}{y}}{y^2}$$

on the other hand equals the 2nd expression you noted.

Multiply top and bottom by $y$ and multiply the two $x$'s to get $x^2$

This results in

$\dfrac{y^2 - x^2}{y^3}$

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Evin

#### Evin

My people will sing songs in your honor for generations to come.

romsek