Question

Answer 1

a: ĐKXĐ: x<>0; x<>2; x<>-2

b: \(Q=\left(\dfrac{x\left(x+2\right)}{x\cdot\left(x-2\right)}-\dfrac{2\left(x-2\right)}{2\left(x+2\right)}\right)\cdot\dfrac{x-2}{4x}\)

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

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

\(=\dfrac{x^2+4x+4-x^2+4x-4}{\left(x+2\right)}\cdot\dfrac{1}{4x}=\dfrac{8x}{4x}\cdot\dfrac{1}{x+2}=\dfrac{2}{x+2}\)

c: Q=1

=>x+2=2

=>x=0(loại)

d: Q<0

=>x+2<0

=>x<-2

e: Q nguyên

=>x+2 thuộc Ư(2)

=>x+2 thuộc {1;-1;2;-2}

=>x thuộc {-1;-3;-4}