Question

допоможіть вирішити
1) a+5 20a
____ + ____ =
a-5 25-a²
2) 2х 2х+12
_______ - _____ =
х²-6х+9 х²-9
3) 6a 21 6a²
____ - ___ +____ =
a-7 a+7 49-a²

Answer 1

Ответ:

Объяснение:

$\displaystyle\\\frac{a+5}{a-5} +\frac{20a}{25-a^2} =\frac{a+5}{a-5} -\frac{20a}{(a-5)(a+5)} =\\\\\\   \frac{(a+5)(a+5)-20a}{(a-5)(a+5)}=\frac{a^2+10a+25-20a}{(a-5)(a+5)} =\\  \\ \\ \frac{(a-5)^2}{(a-5)(a+5)}=\frac{a-5}{a+5}$

$\displaystyle\\\frac{2x}{x^2-6x+9}-\frac{2x+12}{x^2-9} =\frac{2x}{(x-3)(x-3)}-\frac{2x+12}{(x-3)(x+3)} =\\ \\ \\\frac{2x(x+3)-(2x+12)(x-3)}{(x-3)(x-3)(x+3)} = \frac{2x^2+6x-2x^2-6x+36}{(x-3)(x-3)(x+3)}=\\ \\ \\ \frac{36}{(x-3)^2(x+3)}$

$\displaystyle\\\frac{6a}{a-7} -\frac{21}{a+7}+\frac{6a^2}{49-a^2}=\frac{6a(a+7)-21(a-7)-6a^2}{(a-7)(a+7)} =\\ \\ \\\frac{6a^2+42a-21a+147-6a^2}{(a-7)(a+7)} =\frac{21a+147}{(a-7)(a+7)} =\\ \\ \\\frac{21(a+7)}{(a-7)(a+7)}=\frac{21}{a-7}$