Question

решите уравнения 1/х+4-1/х-4=1/х-2-1/х-5

Answer 1

$frac{1}{x+4}- frac{1}{x-4}= frac{1}{x-2}- frac{1}{x-5}\x neq -4;x neq 2;x neq 4;x neq 5\ frac{x-4-x-4}{x^2-16} = frac{x-5-x+2}{(x-2)(x-5)} \frac{-8}{x^2-16} = frac{-3}{(x-2)(x-5)} \-3(x^2-16)=-8(x^2-7x+10)\3x^2-48=8x^2-56x+80\5x^2-56x+128=0\ frac{D}{4} =28^2-5*128=4^2(7^2-5*8)=4^2*9=4^2*3^2=12^2\x_1= frac{28-12}{5} = frac{16}{5}=3,2\x_3= frac{28+12}{5}= frac{40}{5} =8$