Đáp án: `S={0;9/2}`
Giải thích các bước giải:
`x/(x - 3) - x/(x - 5)=x/(x-4)-x/(x-6)(xne3,xne5,xne4,xne6)` $\\$ `<=> [x(x-5)-x(x-3)]/[(x-3)(x-5)]=[x(x-6)-x(x-4)]/[(x-4)(x-6)]` $\\$ `<=> (x^2-5x-x^2+3x)/[(x - 3)(x - 5)] = (x^2 - 6x - x^2 + 4x)/[(x-4)(x-6)]` $\\$ `<=> (-2x)/[(x - 3)(x - 5)] = (-2x)/[(x-4)(x-6)]` $\\$ `<=> (-2x)/[(x - 3)(x - 5)] - (-2x)/[(x - 4)(x - 6)]=0` $\\$ `<=> (-2x)(1/[(x-3)(x-5)] - 1/[(x-4)(x-6)]) = 0`
TH1 : `-2x = 0<=>x=0(tm)`
TH2 : `1/[(x-3)(x-5)] - 1/[(x-4)(x-6)]=0 ` $\\$ `<=> [(x-4)(x-6)-(x-3)(x-5)]/[(x-3)(x-5)(x-4)(x-6)] = 0` $\\$ `=> (x - 4)(x - 6) - (x - 3)(x - 5) = 0` $\\$ `<=> x^2 - 6x - 4x + 24 - (x^2 - 5x - 3x + 15) = 0` $\\$ `<=> x^2 - 6x - 4x + 24 - x^2 + 5x + 3x - 15 = 0` $\\$ `<=> -2x + 9 = 0 <=> -2x = -9 <=> x = 9/2(tm)`
Vậy `S={0;9/2}`
