what algebraic manipulation was used here?

Feb 2020
2
1
Norway
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
 
Last edited:

romsek

Math Team
Sep 2015
2,969
1,677
USA
Afraid your understanding is incorrect.

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

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

$\dfrac{y^2 - x^2}{y^3}$
 
Last edited:
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Feb 2020
2
1
Norway
My people will sing songs in your honor for generations to come.
 
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