Вправи 888 - 1000 » 922 (а-б)

922. Розв’яжи рівняння. a) (x-1)/(x-2) + (x-2)/(x-1) = 5/2, x ≠ 2, x ≠ 1; (〖(x-1)〗^2+〖(x-2)〗^2 )/((x-2)(x-1)) = 5/2; (x^2-2x+1+x^2-4x+4 )/(x^2-2x- x+2) = 5/2; (〖2x〗^2-6x+5)/(x^2-3x+2) = 5/2; 2(2x2 – 6x + 5) = 5(x2 – 3x + 2); 4x2 – 12x + 10 = 5x2 – 15x + 10; 5x2 – 15x + 10 – 4x2 + 12x – 10 = 0; x2 – 3x = 0; x(x – 3) = 0; x = 0, x = 3; б) (x-3)/(x+3) – (x+3)/(3+ x) = 4, x ≠ 3, x ≠ –3; (〖(x-3)〗^2+〖(x+3)〗^2 )/((x+3)(x-3)) = 4; (x^2-6x+9+x^2+6x+9 )/(x^2-9) = 4; (〖2(x〗^2+9))/(x^2-9) = 4; (x^2+9)/(x^2-9) = 2; (x2 – 9) • 2 = x2 + 9; 2x2 – 18 = x2 + 8; x2 = 27; x = ± 3√3.