Question

calculați :
$\frac{ a - b}{a - b + 2c} - \frac{a - b}{a - b + 2c}$

Answer 1

$=\frac{(a-b)(a-b-2c)}{(a-b+2c)(a-b-2c)}-\frac{(a-b)(a-b+2c)}{(a-b-2c)(a-b+2c)}$

$a-b=t$

$=\frac{t(t-2c)}{(t+2c)(t-2c)}-\frac{t(t+2c)}{(t-2c)(t+2c)}$

$=\frac{t(t-2c)-t(t+2c)}{(t-2c)(t+2c)}$

$=\frac{{t}^{2}-2tc-{t}^{2}-2tc}{{t}^{2}-4{c}^{2}}$

$=\frac{-4tc}{{t}^{2}-4{c}^{2}}$

$=-\frac{4c(a-b)}{{(a-b)}^{2}-4 { c}^{2}}$