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

\(=x^2+4x-21-x^2-4x+5\)

=-16

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

\(=3\left(x^2+2x+1\right)+2\left(x^2-6x+9\right)-5\left(x^2-25\right)\)

\(=3x^2+6x+3+2x^2-12x+18-5x^2+125\)

\(=-6x+146\)

a: ĐKXĐ: \(x\notin\left\{1;-1\right\}\)

\(\dfrac{3}{x-1}+\dfrac{5}{x+1}-\dfrac{x}{x^2-1}\)

\(=\dfrac{3}{x-1}+\dfrac{5}{x+1}-\dfrac{x}{\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{3\left(x+1\right)+5\left(x-1\right)-x}{\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{3x+3+5x-5-x}{\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{7x-2}{\left(x-1\right)\left(x+1\right)}\)

Bài 1: 

b: \(=\dfrac{x+3-4-x}{x-2}=\dfrac{-1}{x-2}\)

Bài 2: 

a: \(=\dfrac{x+1}{2\left(x+3\right)}+\dfrac{2x+3}{x\left(x+3\right)}\)

\(=\dfrac{x^2+x+4x+6}{2x\left(x+3\right)}=\dfrac{x^2+5x+6}{2x\left(x+3\right)}=\dfrac{x+2}{2x}\)

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

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

e: \(=\dfrac{x^2+2xy+x^2-2xy-4xy}{\left(x+2y\right)\left(x-2y\right)}=\dfrac{2x^2-4xy}{\left(x+2y\right)\cdot\left(x-2y\right)}=\dfrac{2x}{x+2y}\)

\(=\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{13\cdot15}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{13}-\dfrac{1}{15}=\dfrac{14}{15}\)

\(1,=\left(x+3\right)\left(x-2\right):\left(x+3\right)=x-2\\ 2,=\left(x-5\right)\left(x+6\right):\left(x+6\right)=x-5\\ 3,=\left[3x\left(2x-1\right)-5\right]:\left(2x-1\right)=3x.dư.\left(-5\right)\)

1)\(\left(x+x^2-6\right):\left(x+3\right)=\left[x\left(x+3\right)-2\left(x+3\right)\right]:\left(x+3\right)=\left[\left(x+3\right)\left(x-2\right)\right]:\left(x+3\right)=x-2\)

2) \(\left(x+x^2-30\right):\left(x+6\right)=\left[x\left(x+6\right)-5\left(x+6\right)\right]:\left(x+6\right)=\left[\left(x+6\right)\left(x-5\right)\right]:\left(x+6\right)=x-5\)

3) \(\left(5-3x+6x^2\right):\left(2x-1\right)=\left[3x\left(2x-1\right)+5\right]:\left(2x-1\right)=3x+\dfrac{5}{2x-1}\)

a) \(2x\left(x+5\right)-2x^2=2x^2+10x-2x^2=10x\)

b) \(\left(x+3\right)^2+\left(x-1\right)\left(3+2x\right)=x^2+6x+9+3x+2x^2-3-2x\)

\(=3x^2+7x+6\)

a: \(2x\left(x+5\right)-2x^2=2x^2+10x-2x^2=10x\)

b: \(\left(x+3\right)^2+\left(2x+3\right)\left(x-1\right)\)

\(=x^2+6x+9+2x^2-2x+3x-3\)

\(=3x^2+7x+6\)

câu 1 là (x-y).(6x^2-4y^2+\(\dfrac{1}{2}\)xy) nha 

a/ \(\left(2x+3\right)\left(x-5\right)-\left(x-1\right)^2+x\left(7-x\right)\)

\(=2x^2-2x-15-x^2+2x-1+7x-x^2\)

\(=7x-16\)

b, = x² - 16 - ( x³ - 3³ ) : ( x - 3 )

= x² - 16 - \([\) ( x - 3 ) ( x² + 3x + 9 ) \(]\) : ( x - 3 )

= x² - 16 - ( x² + 3x + 9 )

= x² - 16 - x² - 3x - 9

= -25 - 3x

\(a,=2x^2-10x+3x-15-x^2+2x-1+7x-x^2=2x-16\\ b,=x^2-16-\left(x-3\right)\left(x^2+3x+9\right):\left(x-3\right)\\ =x^2-16-x^2-3x-9=-3x-25\)