Question

cho biểu thức sau: \(A=\left(\dfrac{1}{X-1}-\dfrac{X}{1-X^3}.\dfrac{X^2+X+1}{X+1}\right):\dfrac{2X+1}{X^2+2X+1}\)

a/ Rút gọn biểu thức A?

b/ tính giá trị của A khi x=1/2

Answer 1

a: \(A=\left(\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+x+1}{x+1}\right)\cdot\dfrac{\left(x+1\right)^2}{2x+1}\)

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

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

b: Để A=1/2 thì \(\dfrac{x+1}{x-1}=\dfrac{1}{2}\)

=>2x+2=x-1

=>x=-3(nhận)