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 $\displaystyle \dfrac{a}{b} \in \mathbb{R}$.

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

$\displaystyle \\bc=ad\\-bc=-ad\\ab-bc=ab-ad\text{ adding }ab\\\text{ divide both by }b(b-d)$