Giải pt: a,x-1/x+1/x+1=2x-1/x^2+x b,2x(x-3)+5(x-3)=0

Đáp án:

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`(x-1)/x+1/(x+1)=(2x-1)/(x^2+x)(x\ne0;x\ne-1)`

`=>((x-1)(x+1))/(x(x+1))+x/(x(x+1))=(2x-1)/(x(x+1))`

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

`=>x^2-1+x=2x-1`

`=>x^2+x-2x=-1+1`

`=>x^2-x=0`

`=>x(x-1)=0`

`=>`$\left[\begin{matrix} x=0\\ x-1=0\end{matrix}\right.$

`=>`$\left[\begin{matrix} x=0\\ x=1\end{matrix}\right.$

Vậy `S={0;1}`

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`2x(x-3)+5(x-3)=0`

`=>(x-3)(2x+5)=0`

`=>`$\left[\begin{matrix} x-3=0\\ 2x+5=0\end{matrix}\right.$

`=>`$\left[\begin{matrix} x-3=0\\ 2x=-5\end{matrix}\right.$

`=>`$\left[\begin{matrix} x=3\\ x=\dfrac{-5}{2}\end{matrix}\right.$

Vậy `S={3;-5/2}`

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Đáp án + Giải thích các bước giải:

a)

`(x-1)/x+1/(x+1)=(2x-1)/(x^2+x)(x\ne0;x\ne-1)`

`=>((x-1)(x+1))/(x(x+1))+x/(x(x+1))=(2x-1)/(x(x+1))`

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

`=>x^2-1+x=2x-1`

`=>x^2+x-2x=-1+1`

`=>x^2-x=0`

`=>x(x-1)=0`

`=>x=0` hoặc `x-1=0`

`=>x=0` hoặc `x=1`

Vậy `S={0;1}`

b)

`2x(x-3)+5(x-3)=0`

`=>(x-3)(2x+5)=0`

`=>x-3=0` hoặc `2x+5=0`

`=>x=3` hoặc `2x=-5`

`=>x=3` hoặc `x=-5/2`

Vậy `S={3;-5/2}`