Question

cho biểu thức

\(P=\left[\dfrac{x^2-2x+4}{x-2}\div\left(x^3+8\right)+\dfrac{x-2}{x^3+8}\cdot\dfrac{x^2-2x+4}{x^2-4}\right]\cdot\left(x^2-4\right)\)

a, rút gọn P

b, tính P biết \(x=-\dfrac{1}{2}\)

Answer 1

Lời giải:

ĐK:.....

\(P=\left[\frac{x^2-2x+4}{x-2}.\frac{1}{x^3+8}+\frac{x-2}{x^3+8}.\frac{x^2-2x+4}{x^2-4}\right].(x^2-4)\)

\(P=\left[\frac{x^2-2x+4}{x-2}.\frac{1}{(x+2)(x^2-2x+4)}+\frac{x-2}{(x+2)(x^2-2x+4)}.\frac{x^2-2x+4}{(x-2)(x+2)}\right](x^2-4)\)

\(P=\left[\frac{1}{(x-2)(x+2)}+\frac{1}{(x+2)^2}\right](x^2-4)\)

\(=1+\frac{x^2-4}{(x+2)^2}=1+\frac{x-2}{x+2}=\frac{2x}{x+2}\)

b) Với \(x=-\frac{1}{2}\Rightarrow P=\frac{-2}{3}\)