Question

cho M=\(\left(\dfrac{1}{1-x}+\dfrac{2}{x+1}-\dfrac{5-x}{x^2-1}\right)\) (x khác +-1)

a,rút gọn M

b,tìm x để M=\(-\dfrac{2}{3}\)

Answer 1

\(M=\dfrac{1}{1-x}+\dfrac{2}{x+1}-\dfrac{5-x}{x^2-1}\)

\(\Leftrightarrow M=\dfrac{1}{1-x}+\dfrac{2}{1+x}+\dfrac{5-x}{1-x^2}\)

\(\Leftrightarrow M=\dfrac{1}{1-x}+\dfrac{2}{1+x}+\dfrac{5-x}{\left(1-x\right)\left(1+x\right)}\) MTC: \(\left(1-x\right)\left(1+x\right)\)

\(\Leftrightarrow M=\dfrac{1+x}{\left(1-x\right)\left(1+x\right)}+\dfrac{2\left(1-x\right)}{\left(1-x\right)\left(1+x\right)}+\dfrac{5-x}{\left(1-x\right)\left(1+x\right)}\)

\(\Leftrightarrow M=\dfrac{1+x+2\left(1-x\right)+\left(5-x\right)}{\left(1-x\right)\left(1+x\right)}\)

\(\Leftrightarrow M=\dfrac{1+x+2-2x+5-x}{\left(1-x\right)\left(1+x\right)}\)

\(\Leftrightarrow M=\dfrac{-2x+8}{\left(1-x\right)\left(1+x\right)}\)