Question

Answer 1

a) \(M=\left(\dfrac{4x}{x^2-4}+\dfrac{2x-4}{x+2}\right)\cdot\dfrac{x+2}{2x}+\dfrac{2}{2-x}\) 

\(M=\left[\dfrac{4x}{\left(x+2\right)\left(x-2\right)}+\dfrac{2\left(x-2\right)}{x+2}\right]\cdot\dfrac{x+2}{2x}+\dfrac{2}{2-x}\)

\(M=\left[\dfrac{4x}{\left(x+2\right)\left(x-2\right)}+\dfrac{2\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}\right]\cdot\dfrac{x+2}{2x}+\dfrac{2}{2-x}\)

\(M=\dfrac{4x+2x^2-8x+8}{\left(x+2\right)\left(x-2\right)}\cdot\dfrac{x+2}{2x}+\dfrac{2}{2-x}\)

\(M=\dfrac{2x^2-4x+8}{\left(x+2\right)\left(x-2\right)}\cdot\dfrac{x+2}{2x}\)

\(M=\dfrac{2\left(x^2-2x+4\right)}{\left(x+2\right)\left(x-2\right)}\cdot\dfrac{x+2}{2x}+\dfrac{2}{2-x}\) 

\(M=\dfrac{x^2-2x+4}{x^2-2x}+\dfrac{2}{2-x}\)

\(M=\dfrac{x^2-2x+4}{x\left(x-2\right)}-\dfrac{2x}{x\left(x-2\right)}\)

\(M=\dfrac{x^2-2x+4-2x}{x\left(x-2\right)}\)

\(M=\dfrac{x^2-4x+4}{x\left(x-2\right)}\)

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

\(M=\dfrac{x-2}{x}\)

b) Thay \(x=4\) vào biểu thức ta có

\(M=\dfrac{4-2}{4}=\dfrac{2}{4}=\dfrac{1}{2}\)