(x-1)(x-2)(x+2)-(x-3)\(^3\)

=(x-1)(x\(^2\)-4)-(x-3)\(^3\)

(xy-1)(xy-2)-(xy-2)\(^2\)

=(xy-2)(xy-1-xy+2)

=xy-2

a)2/x+4x+2/x^2-1

b)

Sửa đề: \(P=\left(\dfrac{\sqrt{x}}{\sqrt{x}-2}+\dfrac{\sqrt{x}}{\sqrt{x}+2}\right)\cdot\dfrac{x-4}{4-\sqrt{x}}\)

a: \(P=\dfrac{x+2\sqrt{x}+x-2\sqrt{x}}{x-4}\cdot\dfrac{x-4}{4-\sqrt{x}}=\dfrac{2x}{4-\sqrt{x}}\)

b: Để P>3 thì P-3>0

\(\Leftrightarrow-\dfrac{2x}{\sqrt{x}-4}-3>0\)

\(\Leftrightarrow\dfrac{-2x-3\sqrt{x}+12}{\sqrt{x}-4}>0\)

\(\Leftrightarrow\dfrac{5\sqrt{x}-12}{\sqrt{x}-4}< 0\)

=>12/5<căn x<4

=>144/25<x<16

Ta có: a)(x - 5).(2x +3) - (2x -1).(x +7) - (x -1).(x+2)

= 2x² + 3x - 10x - 15 - 2x² - 14x + x + 7 - x² - 2x + x + 2

= -x² - 21x - 6

\(A=\dfrac{2\sqrt{x}-9}{x-5\sqrt{x}+6}-\dfrac{\sqrt{x}-3}{\sqrt{x}-2}+\dfrac{2\sqrt{x}+1}{\sqrt{x}-3}\)

\(=\dfrac{2\sqrt{x}-9-x+9+2x-4\sqrt{x}+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\)

\(D=\dfrac{5}{2x^2+6x}-\dfrac{4-3x^2}{x^2-9}-3\) (đk:\(x\ne3;x\ne-3\))

\(=\dfrac{5}{2x\left(x+3\right)}-\dfrac{4-3x^2}{\left(x-3\right)\left(x+3\right)}-3\)

\(=\dfrac{5\left(x-3\right)}{2x\left(x-3\right)\left(x+3\right)}-\dfrac{\left(4-3x^2\right).2x}{2x\left(x-3\right)\left(x+3\right)}-\dfrac{3.2x\left(x-3\right)\left(x+3\right)}{2x\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{5x-15-8x+6x^3-6x\left(x^2-9\right)}{2x\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{51x-15}{2x\left(x-3\right)\left(x+3\right)}\)

Ta có: \(\left(x+5\right)\left(x^2-5x+25\right)-\left(x+3\right)^3+\left(x-2\right)\left(x^2+2x+4\right)-\left(x-1\right)^3\)

\(=x^3+125-x^3-9x^2-27x-27+x^3-8-x^3+3x^2-3x+1\)

\(=-6x^2-30x+91\)