Question

P=(\(\dfrac{1}{x-2}_{ }-\dfrac{2x}{4-x^2}+\dfrac{1}{2+x}\)) . (\(\dfrac{2}{x}-1\))

a, rút gọn P

b,tính giá trị P khi |x|=3

c,tìm x để P=1

d,tìm x thuộc Z để P có giá trị nguyên

Answer 1

a, P = \(\left(\dfrac{1}{x-2}-\dfrac{2x}{4-x^2}+\dfrac{1}{2+x}\right)\left(\dfrac{2}{x}-1\right)\)

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

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

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

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

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