# Make x the subject

• May 29th 2010, 09:10 AM
preid
Make x the subject
Hi

Where am I going wrong in trying to rearrange this:

$
\frac{x+a}{x+b} = c
$

$
x+a = c(x+b)
$

$
\frac{x+a}{c} = x+b
$

$
\frac{x+a}{c}-b = x
$

$
x+a - cb = xc
$

$
a - cb = xc - x
$

$
\frac{a-cb}{c} = x - x
$

Thanks
• May 29th 2010, 10:10 AM
Failure
Quote:

Originally Posted by preid
Hi

Where am I going wrong in trying to rearrange this:

$
\frac{x+a}{x+b} = c
$

$
x+a = c(x+b)
$

$
\frac{x+a}{c} = x+b
$

$
\frac{x+a}{c}-b = x
$

$
x+a - cb = xc
$

$
a - cb = xc - x
$

Ok thus far, although a bit longwinded. But now factor out x on the right side first:

$a-cb=x(c-1)$
and divide both sides by $c-1$ to get:

$\frac{a-cb}{c-1}=x$