Question

Упростите выражение:
1)__a-5__+__12__a²-49
a²-49
2)__2a-4__-__2b-4__a²-b²
a²-b²
3)__7a+5b__-__4a+2b__(a-b)²
(a-b)
4)__a²__-__2a-1__a²-1
a²-1

Answer 1

$1) \frac{a-5}{a^2-49} + \frac{12}{a^2-49} = \frac{a-5+12}{(x+7)(x-7)} =\frac{a+7}{(x+7)(x-7)}=\frac{1}{x-7} \\ \\ 2) \frac{2a-4}{a^2-b^2} - \frac{2b-4}{a^2-b^2} = \frac{(2a-4)-(2b-4)}{(a+b)(a-b)} = \frac{2a-4-2b+4}{(a+b)(a-b)}=\frac{2(a-b)}{(a+b)(a-b)}=\frac{2}{a+b}$

$3) \frac{7a+5b}{(a-b)^2} - \frac{4a+2b}{(a-b)^2} = \frac{(7a+5b)-(4a+2b)}{(a-b)^2} =\frac{7a+5b-4a-2b}{(a-b)^2} =\frac{3(a+b)}{(a-b)^2} \\ \\ 4) \frac{a^2}{a^2-1} - \frac{2a-1}{a^2-1} = \frac{a^2-(2a-1)}{(a+1)(a-1)} =\frac{a^2-2a+1}{(a+1)(a-1)} =\frac{(a-1)^2}{(a+1)(a-1)} =\frac{a-1}{a+1}$