Make x the subject

**preid** · May 29th 2010, 09:10 AM

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

**Failure** · May 29th 2010, 10:10 AM

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:

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

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