giải các pt sau:a)2x-3=3.(2x-3)+x+1 b) x(x+1)-(x+2).(x-3)=7 c)x-3/x+1=x^2/x^2-1

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1. Đáp án:

   `a,2x-3=3(2x-3)+x+1`

   `<=>2x-3=6x-9+x+1`

   `<=>2x-3=7x-8`

   `<=>-5x=-5`

   `<=>x=1`

   Vậy `S={1}`

   `b,x(x+1)-(x+2)(x-3)=7`

   `<=>x^2+x-x^2+x+6-7=0`

   `<=>2x-1=0`

   `<=>x=1/2`

   Vậy `S={1/2}`

   `c,(x-3)/(x+1)=(x^2)/(x^2-1)` ĐKXĐ: `x\ne+-1`

   `<=>((x-3)(x-1))/(x^2-1)=(x^2)/(x^2-1)`

   `=>x^2-4x+3=x^2`

   `<=>-4x=-3`

   `<=>x=3/4(\text{tmđk})`

   Vậy `S={3/4}`

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2. `a) 2x-3=3(2x-3)+x+1`

   `<=> 2x-3=6x-9+x+1`

   `<=> 2x-3=7x-8`

   `<=> 7x-2x=-3+8`

   `<=> 5x=5`

   `<=> x=1`

   Vậy `S={1}`

   `b) x(x+1)-(x+2)(x-3)=7`

   `<=> x^2+x-(x^2-3x+2x-6)=7`

   `<=> x^2+x-x^2+x+6=7`

   `<=> 2x=1`

   `<=> x=1/2`

   Vậy `S={1/2}`

   `c) (x-3)/(x+1)=(x^2)/(x^2-1)` (`x \ne +-1`)

   `<=> ((x-3)(x-1))/((x+1)(x-1))=(x^2)/((x-1)(x+1))`

   `=> x^2-x-3x+3=x^2`

   `<=> x^2-x^2+4x=3`

   `<=> 4x=3`

   `<=> x=3/4` (TM)

   Vậy `S={3/4}`

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