A=\(\dfrac{3x^3-14x^2+3x+36}{3x^3-19x^2+33x-9}\)

=>A \(=\dfrac{\left(x-3\right)\left(3x^2-5x-12\right)}{\left(x-3\right)\left(3x^2-10x+3\right)}\)

=>A=\(\dfrac{\left(x-3\right)^2\left(3x+4\right)}{\left(x-3\right)^2\left(3x-1\right)}\)

=>A=\(\dfrac{3x+4}{3x-1}\)

\(\dfrac{\left(2x+1\right)^2}{5}-\dfrac{\left(x-1\right)^2}{3}=\dfrac{7x^2-14x-5}{15}\)

=> \(\dfrac{3\left(4x^2+4x+1\right)-5\left(x^2-2x+1\right)}{15}\) \(=\dfrac{7x^2-14x-5}{15}\)

=> \(\dfrac{7x^2+22x-2}{15}=\dfrac{7x^2-14x-5}{15}\)

=> \(\dfrac{7x^2+22x-2-7x^2+14x+5}{15}=0\)

=>\(\dfrac{36x+3}{15}=0\)

=> 36x=-3

=>\(x=\dfrac{-1}{12}\)

Vay \(S=\left\{\dfrac{-1}{12}\right\}\)

1. \(x^3+6x^2+11x\) +6

= \(x^2\left(x+3\right)+3x\left(x+3\right)+2\left(x+3\right)\)

= \(\left(x+3\right)\left(x^2+3x+2\right)\)

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

2. Sua \(n^3\left(n^2+7\right)^2-36n\) thanh \(n^3\left(n^2-7\right)^2-36n\)

A= \(n^3\left(n^2-7\right)^2-36n\)

= \(n^7-14n^5+49n^3-36n\)

= (n-3)(n-2)(n-1)n(n+1)(n+2)(n+3)

Day la tich cua 7 so tu nhien lien tiep=> A \(⋮105\)

A\(=9x^2+6x-7\)

\(=9\left(x^2+\dfrac{2}{3}x-\dfrac{7}{9}\right)\)

\(=9\left(x^2+2.x.\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{-8}{9}\right)\)

\(=9\left(x+\dfrac{1}{3}\right)^2+\left(-8\right)\)

Vì \(\left(x+\dfrac{1}{3}\right)^2\ge0\)

\(\Rightarrow\left(x+\dfrac{1}{3}\right)^2+\left(-8\right)\ge-8\)

Dấu = xảy ra khi x+\(\dfrac{1}{3}=0\Rightarrow x=\dfrac{-1}{3}\)

Vậy GTNN của A=-8 khi x=\(\dfrac{-1}{3}\)

2) a)\(x\left(x+3\right)-x^2=6\)

\(\Rightarrow x^2+3x-x^2=6\)

\(\Rightarrow\left(x^2-x^2\right)+3x=6\)

\(\Rightarrow3x=6\)

\(\Rightarrow x=2\)

Vậy x=2

b) \(2x\left(x-5\right)+x\left(-2x-1\right)=6\)

\(\Rightarrow2x^2-10x-2x^2-x=6\)

\(\Rightarrow\left(2x^2-2x^2\right)+\left(-10x-x\right)=6\)

\(\Rightarrow-11x=6\)

\(\Rightarrow x=-\dfrac{6}{11}\)

\(\)Vậy \(x=-\dfrac{6}{11}\)

c) x(x+5)-(x+1)(x-2)=7

\(\Rightarrow x^2+5x-x^2+2x-x+2=7\)

\(\Rightarrow\left(x^2-x^2\right)+\left(5x+2x-x\right)=7-2\)

\(\Rightarrow6x=5\)

\(\Rightarrow x=\dfrac{5}{6}\)

Vậy x=\(\dfrac{5}{6}\)

d)\(\left(3x+4\right)\left(6x-3\right)-\left(2x+1\right)\left(9x-2\right)=10\)

\(\Rightarrow18x^2-9x+24x-12-18x^2+4x-9x+2=10\)

\(\Rightarrow\left(18x^2-18x^2\right)+\left(-9x+24x+4x-9x\right)+\left(-12+2\right)=10\)

\(\Rightarrow10x-10=10\)

\(\Rightarrow10x=20\)

\(\Rightarrow x=2\)

Vậy x=2

1) a) \(\left(3x-1\right)\left(9x^2+3x+1\right)-4x\left(x-5\right)\)

\(=27x^3+9x^2+3x-9x^2-3x-1-4x^2+20x\)

\(=27x^3+\left(9x^2-9x^2-4x^2\right)+\left(3x-3x+20x\right)+\left(-1\right)\)

\(=27x^3-4x^2+20x-1\)

b)\(\left(7x+2\right)\left(3-4x\right)-\left(x+3\right)\left(x^2-3x+9\right)\)

\(=21x-28x^2+6-8x-x^3+3x^2-9x-3x^2+9x-27\)

\(=\left(21x-8x-9x+9x\right)+\left(-28x^2+3x^2-3x^2\right)\)\(+\left(6-27\right)\)\(+\left(-x^3\right)\)

\(=13x-28x^2-21-x^3\)

c)\(\left(4x+3\right)\left(4x-3\right)-\left(2-x\right)\left(4+2x+x^2\right)\)

\(=16x^2-12x+12x-9-8-4x-2x^2+4x+2x^2+x^3\)

\(=\left(16x^2-2x^2+2x^2\right)+\left(-12x+12x-4x+4x\right)\)\(+\left(-9-8\right)\)\(+x^3\)

\(=16x^2-17+x^3\)

d)\(\left(3x-8\right)\left(-5x+6\right)-\left(4x+1\right)\left(3x-2\right)\)

\(=-15x^2+18x+40x-48-12x^2+8x-3x+2\)

\(=\left(-15x^2-12x^2\right)+\left(18x+40x+8x-3x\right)\)\(+\left(-48+2\right)\)

\(=-27x^2+63x-46\)

e)\(\left(3x-6\right)4x-2x\left(3x+5\right)-4x^2\)

\(=12x^2-24x-6x^2-10x-4x^2\)

\(=\left(12x^2-6x^2-4x^2\right)+\left(-24x-10x\right)\)

\(=2x^2-34x\)

f)\(\left(5x-6\right)\left(6x-5\right)-x\left(3x+10\right)\)

\(=30x^2-25x-36x+30-3x^2-10x\)

\(=\left(30x^2-3x^2\right)+\left(-25x-36x-10x\right)+30\)

\(=27x^2-71x+30\)

\(\left(10-x^4+3x-4x^2\right)\left(2x+x^3-1\right)\)

\(\Rightarrow20x-2x^5+6x^2-8x^3+10x^3-x^7+3x^4-4x^5-10\)\(+x^4\) -3x\(+4x^2\)

\(\Rightarrow\left(-2x^5-4x^5\right)+\left(6x^2+4x^2\right)+\left(-8x^3+10x^3\right)\)\(+\left(-x^7\right)\) \(+\left(3x^4+x^4\right)\)+(20x-3x)+(-10)

=> \(-6x^5+10x^2+2x^3-x^7+4x^4+17x-10\)

\(7\left(5x-1\right)\left(4x+3\right)\)

\(\Rightarrow\left(35x-7\right)\left(4x+3\right)\)

\(\Rightarrow140x^2+105x-28x-21\)

\(\Rightarrow140x^2+77x-21\)