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

Thay \(m=3\) vào \(\left(1\right)\)

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

\(\Rightarrow x^2+3x+2=0\)

\(\Rightarrow x^2+x+2x+2=0\)

\(\Rightarrow x\left(x+1\right)+2\left(x+1\right)=0\)

\(\Rightarrow\left(x+2\right)\left(x+1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x+2=0\\x+1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=-2\\x=-1\end{matrix}\right.\)

Vậy \(S=\left\{-2;-1\right\}\) khi \(m=3\)

7,x²-2xy+y²+3x-3y=(x-y)²+3(x-y)=(x-y)(x-y+3)

8,x⁴+4=(x⁴+4x²+4)-4x²=(x²+2)²-(2x)²=(x²-2x+2)(x²+2x+2)

9,4x(x+1)²-5x²(x+1)-4.(x+1)=(x+1)\(\left[4x\left(x+1\right)-5x^2-4\right]\)=(x+1)(4x²+4x-5x²-4)=(x+1)(-x²+4x-4)=-(x+1)(x-2)²

7: \(x^2-2xy+y^2+3x-3y\)

\(=\left(x-y\right)^2+3\cdot\left(x-y\right)\)

\(=\left(x-y\right)\left(x-y+3\right)\)

8: \(x^4+4\)

\(=x^4+4x^2+4-4x^2\)

\(=\left(x^2+2\right)^2-4x^2\)

\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)

9: \(4x\left(x+1\right)^2-5x^2\left(x+1\right)-4\left(x+1\right)\)

\(=\left(x+1\right)\left(4x^2+4x-5x^2-4\right)\)

\(=\left(x+1\right)\left(-x^2+4x-4\right)\)

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

10: \(\left(1+2x\right)\left(1-2x\right)-\left(x+2\right)\left(x-2\right)\)

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

\(=-5x^2+5\)

\(=-5\left(x-1\right)\left(x+1\right)\)

( x + 1/3 - 1/4 ) : ( 2 + 1/6 - 1/4 ) = 7/46

( x + 1/3 - 1/4 ) : ( 13/6 - 1/4 ) = 7/46

( x + 1/3 - 1/4 ) : 23/12 = 7/46

x + 1/3 - 1/4 = 7/46 x 23/12

x + 1/3 - 1/4 = 7/24

x + 1/3 = 7/24 + 1/4

x + 1/3 = 13/24

        x = 13/24 - 1/3

        x = 5/24

(x + 1/12) : 23/12 = 7/46

(x+1/12) = 7/46 . 23/12

x + 1/12 = 7/24

x = 7/24 - 1/12

x = 5/24

x=3/8