\(\frac{x}{2}-\frac{1}{3}=\frac{1}{y}\)

\(\Leftrightarrow\frac{x}{2}-\frac{1}{y}=\frac{1}{3}\)

\(\Leftrightarrow\frac{xy}{2y}-\frac{2}{2y}=\frac{1}{3}\)

\(\Leftrightarrow\frac{xy-2}{2y}=\frac{1}{3}\)

\(\Leftrightarrow3\left(xy-2\right)=2y\)

\(\Leftrightarrow3xy-6=2y\)

\(\Leftrightarrow3xy-2y=6\)

\(\Leftrightarrow y\left(3x-2\right)=6=1.6=2.3=3.2=6.1=\left(-1\right).\left(-6\right)=\left(-3\right).\left(-2\right)\)

                                                                                               \(=\left(-2\right).\left(-3\right)=\left(-6\right).\left(-1\right)\)

Tự xét bảng giá trị nhé

x² + 2x chia hết cho x + 1

Mà x.(x + 1) chia hết cho x + 1

hay x² + x chia hết cho x + 1

=> [(x² + 2x) - (x² + x)] chia hết cho x + 1

=> x chia hết cho x + 1

=> x + 1 - 1 chia hết cho x + 1

Mà x + 1 chia hết cho x + 1

=> 1 chia hết cho x + 1

=> x + 1 thuộc Ư (1) = {-1; 1}

=> x thuộc {-2; 0}.

(x+1)(x-2)(x-3)(2x-1)(3x-1)=0

\(\Leftrightarrow\) \(6x^5-12x^4-17x^4+34x^3-7x^3+14x^2+13x^2-26x-3x+\)6 =0

\(6x^5-29x^4+27x^3+27x^2-29x+6=0\)

\(\Leftrightarrow\left(6x^5-18x^4\right)+\left(-11x^4+33x^3\right)+\left(-6x^3+18x^2\right)+\left(9x^2-27x\right)+\left(-2x+6\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(6x^4-11x^3-6x^2+9x-2\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(\left(6x^4-12x^3\right)+\left(x^3-2x^2\right)+\left(-4x^2+8x\right)+\left(x-2\right)\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(6x^3+x^2-4x+1\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(\left(6x^3+6x^2\right)+\left(-5x^2-5x\right)+\left(x+1\right)\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(x+1\right)\left(6x^2-5x+1\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(x+1\right)\left(\left(6x^2-3x\right)+\left(-2x+1\right)\right)=0\)

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

\(\Leftrightarrow x=\left(3;2;-1;\frac{1}{2};\frac{1}{3}\right)\)