Question

x-3/x+1=x²/x²-1

Answer 1

\(\dfrac{x-3}{x+1}=\dfrac{x^2}{x^2-1}\left(x\ne-1;x\ne1\right)\\ < =>\dfrac{\left(x-3\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{x^2}{\left(x-1\right)\left(x+1\right)}\)

suy ra

`(x-3)(x-1)=x^2`

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

`<=> x^2 -x^2 -x-3x+3=0`

`<=>-4x=-3`

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

Answer 2

\(\dfrac{x-3}{x+1}=\dfrac{x^2}{x^2-1}\)

\(ĐKXĐ:x+1\ne0\)

\(x\ne-1\)

\(x-1\ne0\)

\(x\ne1\)

\(\Leftrightarrow\left(x-3\right)\left(x-1\right)=x^2\)

\(\Leftrightarrow x^2-4x+3-x^2=0\)

\(\Leftrightarrow-4x+3=0\)

\(\Leftrightarrow-4x=-3\)

\(\Leftrightarrow x=\dfrac{3}{4}\)(nhận)

\(S=\left\{\dfrac{3}{4}\right\}\)