Question

Giải phương trình :

1/x+1 + 2/x³-x²-x+1 = 3/1-x²

Answer 1

từ pt ta có : (x-1)² + 2=3(x-1)

\(\Leftrightarrow\) x²-2x+3=3x-3\(\Leftrightarrow\) x² - 5x +6 =0

\(\Leftrightarrow\) (x-2)(x-3)=0\(\Leftrightarrow\) x=2;x=3

Vây có tập nghiệm là x=2;x=3

Answer 2

\(\frac{1}{x+1}+\frac{2}{x^3-x^2-x+1}=\frac{3}{1-x^2}\) (ĐKXĐ: \(x\ne1;-1\))

\(\Leftrightarrow\frac{1}{x+1}+\frac{2}{\left(x-1\right)\left(x^2-1\right)}=-\frac{3}{x^2-1}\)

\(\Leftrightarrow\frac{\left(x-1\right)^2}{\left(x-1\right)^2\left(x+1\right)}+\frac{2}{\left(x-1\right)^2\left(x+1\right)}=-\frac{3}{x^2-1}\)

\(\Leftrightarrow\frac{x^2+1-2x+2}{\left(x-1\right)^2\left(x+1\right)}=-\frac{3}{x^2-1}\)

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

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

\(\Leftrightarrow x^2+x=0\)

\(\Leftrightarrow x\left(x+1\right)=0\)

\(\Rightarrow\left[\begin{matrix}x=0\left(TM\right)\\x+1=0\left(KTM\right)\end{matrix}\right.\)

Vậy ...