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)²
4)__a²__-__2a-1__
a²-1 a²-1

Answer 1

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

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