Question

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

Answer 1

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



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