algebra expression help

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

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

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

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

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

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