Question

решите уравнение x²+13x /x-4 =x²-15 /4-x .

Answer 1

$frac{x^2+13x}{x-4} = frac{x^2-15}{4-x}\\ frac{x^2+13x}{x-4} - frac{x^2-15}{4-x}=0\\ frac{x^2+13x}{x-4} + frac{x^2-15}{x-4}=0; ; |*x-4 neq 0,; ; x neq 4\\x^2+13x+x^2-15=0\\2x^2+13x-15=0\\D=13^2-4*2*(-15)=169+120=289=17^2\\x_1= frac{-13+17}{2*2} = frac{4}{4}=1;; ; x_2= frac{-13-17}{2*2}= frac{-30}{4}=-7,5$