# algebra expression help

• November 23rd 2013, 11:59 AM
Tweety
algebra expression help
a,b,c and dare real numbers such that

$\frac{a}{b} = \frac{c}{d}$ and b does not equal d,
show that

$\frac{a-c}{b-d} = \frac{a}{b}$

if i multiply by both sides by bd I get ad = bc so ad-bc = 0,

thats as far as i can go..any help appreciated.

thank you.
• November 23rd 2013, 12:51 PM
SlipEternal
Re: algebra expression help
$\dfrac{a-c}{b-d} = \dfrac{a}{b}$ if and only if $b(a-c) = a(b-d)$ and $b-d \neq 0$ and $b\neq 0$. You know $b-d \neq 0$ since $b \neq d$ and $b \neq 0$ since $\dfrac{a}{b} \in \mathbb{R}$.
• November 23rd 2013, 02:25 PM
Plato
Re: algebra expression help
Quote:

Originally Posted by Tweety
a,b,c and are real numbers such that
$\frac{a}{b} = \frac{c}{d}$ and b does not equal d,
show that
$\frac{a-c}{b-d} = \frac{a}{b}$

Here is a slightly different way.
From $\frac{a}{b} = \frac{c}{d}$you can see that
$\\bc=ad\\-bc=-ad\\ab-bc=ab-ad\text{ adding }ab\\\text{ divide both by }b(b-d)$