Вправи 888 - 1000 » 921

921. Розв’яжи рівняння. a) x/(x+3) – x/(x-3) = 4; (x(x-3)+ x(x+3))/((x+3)(x-3)) = 4; (x^2-3x+x^2+3x )/(x^2-9) = 4; 〖2x〗^2/(x^2-9) = 4, x ≠ ± 3; 2x2 = 4x2 – 36; 2x2 = 36; x2 = 18; x = ± √18; б) (x+2)/(x-2) + (x-2)/(x+2) = 31/3; (〖(x+2)〗^2+(〖x-2)〗^2 )/((x-2)(x+2)) = 10/3; (x^2+4x+4+ x^2-4x+4)/(x^2-4) = 10/3; (〖2(x〗^2+4))/(x^2-4) = 10/3, x ≠ ± 2; 3(x2 + 4) = 5(x2 – 4); 3x2 + 12 = 5x2 – 20; 12 + 20 = 5x2 – 3x2; 2x2 = 32; x2 = 16; x = ± 4.