Question

21 баллов даю. Пожалуйста помогите с алгеброй!!!!

Answer 1

$1)(\frac{6a}{2a+5} - \frac{16a}{4a^2+20a + 25} ): \frac{6a+7}{4a^2 - 25} + \frac{10a - 25}{2a+5} = 2a - 5 \\ \\ (\frac{6a}{2a+5} - \frac{16a}{(2a)^2+2*2a*5+ 5^2} ): \frac{6a+7}{(2a)^2 - 5^2} + \frac{5(2a - 5)}{2a+5} = 2a - 5 \\ \\ (\frac{6a}{2a+5} - \frac{16a}{(2a + 5)^2} ): \frac{6a+7}{(2a-5)(2a+5)} + \frac{5(2a - 5)}{2a+5} = 2a - 5 \\ \\ \frac{6a(2a+5)-16a}{(2a+5)^2} : \frac{6a+7}{(2a-5)(2a+5)} + \frac{5(2a - 5)}{2a+5} = 2a - 5$
$\frac{12a^2+30a-16a}{(2a+5)^2} : \frac{6a+7}{(2a-5)(2a+5)} + \frac{5(2a - 5)}{2a+5} = 2a - 5 \\ \\ \frac{12a^2+14a}{(2a+5)^2} : \frac{6a+7}{(2a-5)(2a+5)} + \frac{5(2a - 5)}{2a+5} = 2a - 5 \\ \\ \frac{2a(6a+7)}{(2a+5)(2a+5)} * \frac{(2a-5)(2a+5)}{6a+7} + \frac{5(2a - 5)}{2a+5} = 2a - 5 \\ \\ \frac{2a(6a+7)(2a-5)(2a+5)}{(2a+5)(2a+5)(6a+7)} + \frac{5(2a - 5)}{2a+5} = 2a - 5 \\ \\ \frac{2a(2a-5)}{2a+5} + \frac{5(2a - 5)}{2a+5} = 2a - 5$
$\frac{2a(2a-5)+5(2a-5)}{2a+5} =2a-5 \\ \\ \frac{(2a-5)(2a+5)}{2a+5} = 2a-5 \\ \\ \frac{2a-5}{1} = 2a-5 \\ \\ 2a - 5 = 2a - 5$



$2) (\frac{5x}{x - 10} + \frac{20x}{x^2 - 20x + 100} ) : \frac{4x-24}{x^2 - 100} - \frac{25x}{x-10} = \frac{5x}{4} \\ \\ (\frac{5x}{x - 10} + \frac{20x}{x^2 - 2*x*10+ 10^2} ) : \frac{4(x-6)}{x^2 - 10^2} - \frac{25x}{x-10} = \frac{5x}{4} \\ \\ (\frac{5x}{x - 10} + \frac{20x}{(x-10)^2} ) : \frac{4(x-6)}{(x-10)(x+10)} - \frac{25x}{x-10} = \frac{5x}{4} \\ \\ \frac{5x(x-10)+20x}{(x - 10)^2} * \frac{(x-10)(x+10)}{4(x-6)} - \frac{25x}{x-10} = \frac{5x}{4}$
$\frac{5x^2-50x+20x}{(x - 10)^2} * \frac{(x-10)(x+10)}{4(x-6)} - \frac{25x}{x-10} = \frac{5x}{4} \\ \\ \frac{5x^2-30x}{(x - 10)(x-10)} * \frac{(x-10)(x+10)}{4(x-6)} - \frac{25x}{x-10} = \frac{5x}{4} \\ \\ \frac{5x(x-6)*(x-10)(x+10)}{(x - 10)(x-10)*4(x-6)} - \frac{25x}{x-10} = \frac{5x}{4} \\ \\ \frac{5x(x+10)}{4(x-10)} - \frac{25x}{x-10} = \frac{5x}{4}$
$\frac{5x^2+50x -25x*4}{4(x-10)} = \frac{5x}{4} \\ \\ \frac{5x^2+50x -100x}{4(x-10)} = \frac{5x}{4} \\ \\ \frac{5x^2-50x}{4(x-10)} = \frac{5x}{4} \\ \\ \frac{5x(x-10)}{4(x-10)} = \frac{5x}{4} \\ \\ \frac{5x}{4} = \frac{5x}{4}$