# Trouble understanding rewriting of an expression

• March 22nd 2013, 11:52 AM
dipsy34
Trouble understanding rewriting of an expression
I'm trying to inverse a simple function but got stuck with some algebra I cant remember.

I've got f (x) = 2x-1/x -1 and so far rewritten it to y(x-1) = 2x-1 but got stuck here. Reading the solution it show the next step as (y-2)x=y-1 but I'm at a loss trying to understand how they arrived here.(Headbang)
• March 22nd 2013, 12:19 PM
emakarov
Re: Trouble understanding rewriting of an expression
Quote:

Originally Posted by dipsy34
I'm trying to inverse a simple function but got stuck with some algebra I cant remember.

I've got f (x) = 2x-1/x -1

The first think you need to recall is the order of operations.
• March 22nd 2013, 12:20 PM
earboth
Re: Trouble understanding rewriting of an expression
Quote:

Originally Posted by dipsy34
I'm trying to inverse a simple function but got stuck with some algebra I cant remember.

I've got f (x) = 2x-1/x -1 and so far rewritten it to y(x-1) = 2x-1 but got stuck here. Reading the solution it show the next step as (y-2)x=y-1 but I'm at a loss trying to understand how they arrived here.(Headbang)

I assume that you mean

$y=\frac{2x-1}{x-1}$ ............. If so:

$\begin{array}{rcl}y(x-1)&=&2x-1 \\ yx-y&=&2x-1 \\ 1-y&=& 2x-yx \\ 1-y&=&(2-y) x \\ \frac{1-y}{2-y}&=&x \end{array}$
• March 22nd 2013, 01:18 PM
dipsy34
Re: Trouble understanding rewriting of an expression
Quote:

Originally Posted by earboth
I assume that you mean

$y=\frac{2x-1}{x-1}$ ............. If so:

$\begin{array}{rcl}y(x-1)&=&2x-1 \\ yx-y&=&2x-1 \\ 1-y&=& 2x-yx \\ 1-y&=&(2-y) x \\ \frac{1-y}{2-y}&=&x \end{array}$

Super, thanks.