\(2x-124=x+224\\ \Rightarrow2x+x=224+124\\ \Rightarrow3x=348\\ \Rightarrow x=348:3\\ \Rightarrow x=116\)

\(\dfrac{x+2014}{2}+\dfrac{2x+4028}{7}=\dfrac{x+2014}{5}+\dfrac{x+2014}{6}\\ \Rightarrow\dfrac{x+2014}{2}+\dfrac{x+2014}{7}-\dfrac{x+2014}{5}-\dfrac{x+2014}{6}=0\\ \Rightarrow\left(x+2014\right)\left(\dfrac{1}{2}+\dfrac{1}{7}-\dfrac{1}{5}-\dfrac{1}{6}\right)=0\\\Rightarrow x+2014=0\left(\dfrac{1}{2}+\dfrac{1}{7}-\dfrac{1}{5}-\dfrac{1}{6}\ne0\right)\\ \Rightarrow x=0-2014\\ \Rightarrow x=-2014\)

Chọn `x=-2014`

\(x+\dfrac{3}{4}=\dfrac{1}{2}+\dfrac{9}{8}\\ x+\dfrac{3}{4}=\dfrac{4}{8}+\dfrac{9}{8}\\ x+\dfrac{3}{4}=\dfrac{13}{8}\\ x=\dfrac{13}{8}-\dfrac{3}{4}\\ x=\dfrac{13}{8}-\dfrac{6}{8}\\ x=\dfrac{7}{8}\)

`(xy +1) (x^2y^2 -xy+1) +(x^3-1)(1-y^3)`

`= x^3y^3 - x^2y^2 +xy +x^2y^2 -xy+1 + x^3 -x^3y^3 -1+y^3`

`= (x^3y^3 -x^3y^3) +(-x^2y^2+x^2y^2) +(xy-xy) +x^3+y^3`

`=x^+y^3(đpcm)`

`a, P=x(3x+2) -x(x^2 +3x) +x^3 -2x+3`

`= 3x^2 +2x-(x^3 +3x^2) +x^3-2x+3`

`=3x^2+2x-x^3-3x^2+x^3-2x+3`

`= 3`

`->` Vậy biểu thức không phụ thuộc vào biến.

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`b, Q=x(2x-3) +6x(1/2 -1/3x)+1`

`= 2x^2 -3x+ (6x)/2 - (6x^2)/3 +1`

`= 2x^2 -3x+ 3x - 2x^2 +1`

`=1`

`->` Vậy biểu thức không phụ thuộc vào biến.