Question

Cho phân thức A=x²+x-2/x²-2x+1.Tìm x để:

a,A có nghĩa b,A=0 c,A=1

Answer 1

a/ Ta có :
\(A=\dfrac{x^2+x-2}{x^2-2x+1}\)

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

\(=\dfrac{x\left(x-1\right)+2\left(x-1\right)}{x\left(x-1\right)-\left(x-1\right)}\)

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

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

Để A có nghĩa thì \(x-1\ne0\Leftrightarrow x\ne1\)

b/ Ta có : \(A=0\)

\(\Leftrightarrow\dfrac{x+2}{x-1}=0\)

\(\Leftrightarrow x+2=0\)

\(\Leftrightarrow x=-2\)

Vậy...

c/ Ta có : \(A=1\)

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

\(\Leftrightarrow\dfrac{x+2}{x-1}-1=0\)

\(\Leftrightarrow\dfrac{x+2-x+1}{x-1}=0\)

\(\Leftrightarrow\dfrac{3}{x-1}=0\)

\(\Leftrightarrow3=0\left(vôlys\right)\)

Vậy..