isabelle2hot
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- Nov 21, 2005
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(x-1 - y-1)/(x-1 + 2y-1) = (x + 2y)/(y - x) ????????
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- Thread starter isabelle2hot
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Hello, isabelle2hot!
Multiply top and bottom by \(\displaystyle xy:\;\;\L\frac{xy\left(\frac{1}{x}\,-\,\frac{1}{y}\right)}{xy\left(\frac{1}{x}\,+\,\frac{2}{y}\right)} \;=\;\frac{xy\left(\frac{1}{x}\right)\,-\,xy\left(\frac{1}{y}\right)}{xy\left(\frac{1}{x}\right)\,+\,xy\left(\frac{2}{y}\right)}\)
. . which simplifies to: .\(\displaystyle \L\frac{y\,-\,x}{y\,+\,2x}\)
We have: .\(\displaystyle \L\frac{\frac{1}{x}\,-\,\frac{1}{y}}{\frac{1}{x}\,+\,\frac{2}{y}}\)\(\displaystyle \L\frac{x^{-1}\,-\,y^{-1}}{x^{-1}\,+\,2y^{-1}}\;=\;\)(x + 2y)/(y - x) ?? . . . . they don't "move" like that!
Multiply top and bottom by \(\displaystyle xy:\;\;\L\frac{xy\left(\frac{1}{x}\,-\,\frac{1}{y}\right)}{xy\left(\frac{1}{x}\,+\,\frac{2}{y}\right)} \;=\;\frac{xy\left(\frac{1}{x}\right)\,-\,xy\left(\frac{1}{y}\right)}{xy\left(\frac{1}{x}\right)\,+\,xy\left(\frac{2}{y}\right)}\)
. . which simplifies to: .\(\displaystyle \L\frac{y\,-\,x}{y\,+\,2x}\)