XP Math Games Arcade

06-13-2007

While trying to determine the inverse of (1) y = (1-2x) / (1+x), replace x with y and vice-versa.

(2) This gives x = (1-2y) / (1+y)

The goal is to isolate y in (2), a simple task... however I seem to have forgotten how to do such simple isolations. This part of the problem was skipped in my solutions manual.

The final answer is y = (1-x) / (2+x)

How would one go about solving for y from the original equation?

Thank you for your time.

Mr. Hui · 06-13-2007

$x=\frac{1-2y}{1+y}$ Start

$x+xy=1-2y$ Multiply $(1+y)$ to both sides

$xy+2y=1-x$ Add $2y$ and subtract $x$ to both sides

$y(x+2)=1-x$ Factor out $y$

$y=\frac{1-x}{x+2}$ Divide $(x+2)$ to both sides

06-13-2007

Ther would be excluded values of
$x=-2$ and $y=-1$ . There's others if you solve for some, but...

06-14-2007

Thank you... a little embarrassing how easy it was really

06-13-2007	#1
YvesBenoit Guest Posts: n/a	Easy problem... frustrated! While trying to determine the inverse of (1) y = (1-2x) / (1+x), replace x with y and vice-versa. (2) This gives x = (1-2y) / (1+y) The goal is to isolate y in (2), a simple task... however I seem to have forgotten how to do such simple isolations. This part of the problem was skipped in my solutions manual. The final answer is y = (1-x) / (2+x) How would one go about solving for y from the original equation? Thank you for your time.

06-13-2007	#2
Mr. Hui Join Date: Mar 2005 Posts: 10,609	$x=\frac{1-2y}{1+y}$ Start $x+xy=1-2y$ Multiply $(1+y)$ to both sides $xy+2y=1-x$ Add $2y$ and subtract $x$ to both sides $y(x+2)=1-x$ Factor out $y$ $y=\frac{1-x}{x+2}$ Divide $(x+2)$ to both sides __________________ Do Math and you can do Anything!

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