Question

E=\(\left(\dfrac{2}{1+2x}+\dfrac{4x^2}{4x^2-1}-\dfrac{1}{1-2x}\right):\left(\dfrac{1}{2x-1}-\dfrac{1}{2x+1}\right)\)

a,Rút gọn

b,tính x để E>3

c,Tính Min B

Answer 1

a) Rút gọn

\(E=\left(\dfrac{2}{1+2x}+\dfrac{4x^2}{4x^2-1}+\dfrac{1}{2x-1}\right):\left(\dfrac{1}{2x-1}-\dfrac{1}{2x+1}\right)\)

\(E=\left[\dfrac{2\left(2x-1\right)}{\left(1+2x\right)\left(2x-1\right)}+\dfrac{4x^2}{\left(1+2x\right)\left(2x-1\right)}+\dfrac{1+2x}{\left(1+2x\right)\left(2x-1\right)}\right]:\left(\dfrac{2x+1}{\left(2x-1\right)\left(2x+1\right)}-\dfrac{2x-1}{\left(2x-1\right)\left(2x+1\right)}\right)\)

\(E=\left(\dfrac{4x-2+4x^2+1+2x}{\left(1+2x\right)\left(2x-1\right)}\right):\left(\dfrac{2x+1-2x+1}{\left(2x-1\right)\left(2x+1\right)}\right)\)

\(E=\left(\dfrac{4x^2+6x-1}{\left(1+2x\right)\left(2x-1\right)}\right).\left(\dfrac{\left(2x-1\right)\left(2x+1\right)}{2}\right)\)

\(E=\dfrac{4x^2+6x-1}{2}\)