Simplifying x=d+(p/e)x to x=d/(1+(p/e))

[flakine]

Could someone explain how x=d+(p/e)x, becomes x=d/(1+(p/e))???

 

[soroban]

Re: Simplifying

Hello, flakine!

Could someone explain how \(\displaystyle \L x\:=\:d\,+\.\frac{p}{e}\cdot x\) becomes \(\displaystyle \L x\:=\:\frac{d}{1\,+\,\frac{p}{e}}\) ?
But those two expressions are not equal.

If we are given: \(\displaystyle \:\L x\;=\;d\,+\,\frac{p}{e}\cdot x\)

. . then we have: \(\displaystyle \L\:x\,-\,\frac{p}{e}\cdot x \;=\;d\)

Factor: \(\displaystyle \L\L\left(1\,-\,\frac{p}{e}\right)x\;=\;d\)

Therefore: \(\displaystyle \L\:x\;=\;\frac{d}{1\,-\,\frac{p}{e}}\)

 

[flakine]

Thanks, my text book must have an error.