\(\left(x-2\right)^3\)+\(\left(x+1\right)^3\)+\(\left(1-2x\right)^3\) = 0

\(x^3-6x^2+12x-8+x^3+3x^2+3x+1+1-6x+12x^2-8x^3\text{=}0\)

\(-6x^3+9x^2+9x-6\text{=}0\)

\(\left(-6x^3-6\right).\left(9x^2+9x\right)\text{=}0\)

\(6\left(-x^2-1\right)+9x\left(x+1\right)\text{=}0\)

\(6\left(x-1\right)\left(x+1\right)+9x\left(x+1\right)\text{=}0\)

\([6(x-1)+9x].\left(x+1\right)\text{=}0\)

\(\left(6x-6+9x\right).\left(x+1\right)\text{=}0\)

\(\left(15x-6\right)\left(x+1\right)\text{=}0\)

\(TH1:15x-6\text{=}0\)

            \(15x\text{=}6\)

            \(x\text{=}\dfrac{2}{5}\)

\(TH2:x+1\text{=}0\)

           \(x\text{=}-1\)

Vậy phương trình một ẩn x có tập nghiệm S \(\in(\dfrac{2}{5};-1)\)

bạn mở rộng, bỏ ngoặc, rút gọn có đa thức 6x³ . ...  Đa thức này có nghiệm là  - 1, nhẩm ra , bạn chia đa thức 6 x³  .... với (x + 1)

\(\dfrac{5xy^2}{3xy}+\dfrac{5y^{2} x}{3xy}\)

\(=\dfrac{5xy^{2}+5y^{2}x}{3xy}\)

\(=\dfrac{10xy^{2}}{3xy}=\dfrac{10y}{3}\)

\(x-\dfrac{\dfrac{x}{3}-\dfrac{3+x}{2}}{4}=\dfrac{x-\dfrac{15-7x}{3}}{4}-2x+3\)

\(<=>4x-\dfrac{x}{3}+\dfrac{3+x}{2}=x-\dfrac{15-7x}{3}-8x+12\)

`<=>24x-2x+3(3+x)=6x-2(15-7x)-48x+72`

`<=>24x-2x+9+3x=6x-30+14x-48x+72`

`<=>53x=33`

`<=>x=33/53`

a. \(x\ne5\) là ĐKXĐ của biểu thức P

b. P =\(\dfrac{\left(x-5\right)^2}{x-5}\)=\(x-5\)

c. P = -1 <=> x-5 =-1 <=> x=4

\(\dfrac{x}{x-5}+\dfrac{4x}{x+5}+\dfrac{x\left(x-15\right)}{x^2-25}\)

  = \(\dfrac{x\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}+\dfrac{4x\left(x-5\right)}{\left(x+5\right)\left(x-5\right)}+\dfrac{x\left(x-15\right)}{\left(x+5\right)\left(x-5\right)}\)

  = \(\dfrac{x^2+5x+4x^2-20x+x^2-15x}{\left(x-5\right)\left(x+5\right)}\)

  = \(\dfrac{6x^2-30x}{\left(x-5\right)\left(x+5\right)}\)

  = \(\dfrac{6x\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}\)

  = \(\dfrac{6x}{x+5}\)

\(đk:x\ne1\\ \dfrac{x^2+5x}{3x^2-6x+3}:\dfrac{7x+35}{6x-6}\\ =\dfrac{x\left(x+5\right)}{3\left(x^2-2x+1\right)}:\dfrac{7\left(x+5\right)}{6\left(x-1\right)}\\ =\dfrac{x\left(x+5\right)}{3\left(x-1\right)^2}\times\dfrac{6\left(x-1\right)}{7\left(x+5\right)}\\ =\dfrac{2x}{7\left(x-1\right)}\)

\(đk:x\ne1\)

\(\dfrac{x^2+5}{3x^2-6x+3}.\dfrac{7x+35}{6x-6}\\ =\dfrac{x^2+5}{3\left(x^2-2x+1\right)}.\dfrac{7\left(x+5\right)}{6\left(x-1\right)}\\ =\dfrac{x^2+5}{3\left(x-1\right)^2}.\dfrac{7\left(x+5\right)}{6\left(x-1\right)}\\ =\dfrac{7\left(x^2+5\right)\left(x+5\right)}{18.\left(x-1\right)^3}\)

\(đk:x\ne0;1;-1\\ \dfrac{x^2+x}{x^2-x}.\dfrac{2x^2-2x}{x+1}\\ =\dfrac{x\left(x+1\right)}{x\left(x-1\right)}.\dfrac{2x\left(x-1\right)}{x+1}\\ =2x\)

\(đk:x\ne1\\ \dfrac{3x}{x-1}-\dfrac{5x+1}{2x-2}\\ =\dfrac{3x}{x-1}-\dfrac{5x+1}{2\left(x-1\right)}\\ =\dfrac{2.3x}{2\left(x-1\right)}-\dfrac{5x+1}{2\left(x-1\right)}\\ =\dfrac{6x-5x-1}{2\left(x-1\right)}\\ =\dfrac{x-1}{2\left(x-1\right)}\\ =\dfrac{1}{2}\)