Đáp án:
\(P=\dfrac{8x^{2}-4x^{3}}{(2+x)(x-3)}\)
Giải thích các bước giải:
\(P=\bigg(\dfrac{2+x}{2-x}+\dfrac{4x^{2}}{x^{2}-4}-\dfrac{2-x}{2+x}\bigg):\dfrac{x^{2}-3x}{2x^{2}-x^{3}}\\ =\bigg(\dfrac{(2+x)^{2}}{(2-x)(2+x)}-\dfrac{4x^{2}}{(2-x)(2+x)}-\dfrac{(2-x)^{2}}{(2-x)(2+x)}\bigg):\dfrac{x^{2}-3x}{2x^{2}-x^{3}}\\ =\dfrac{(2+x)^{2}-4x^{2}-(2-x)^{2}}{(2-x)(2+x)}:\dfrac{x^{2}-3x}{2x^{2}-x^{3}}\\ =\dfrac{4+4x+x^{2}-4x^{2}-4+4x-x^{2}}{(2-x)(2+x)}:\dfrac{x(x-3)}{x^{2}(2-x)}\\ =\dfrac{(4-4)+(4x+4x)+(x^{2}-4x^{2}-x^{2})}{(2-x)(2+x)}:\dfrac{x(x-3)}{x^{2}(2-x)}\\ =\dfrac{8x-4x^{2}}{(2-x)(2+x)}:\dfrac{x(x-3)}{x^{2}(2-x)}\\ =\dfrac{4x(2-x)}{(2-x)(2+x)}\times \dfrac{x^{2}(2-x)}{x(x-3)}\\ =\dfrac{4x(2-x).x^{2}(2-x)}{(2-x)(2+x).x(x-3)}\\ =\dfrac{4x^{2}(2-x)}{(2+x)(x-3)}\\ =\dfrac{8x^{2}-4x^{3}}{(2+x)(x-3)}\)
chúc bạn học tốt!
