\(a,=\dfrac{\left(x+1\right)\left(x+y\right)}{\left(x-y\right)\left(x+1\right)}=\dfrac{x+y}{x-y}\\ b,=\dfrac{\left(x-3\right)^2}{3x\left(x-3\right)}=\dfrac{x-3}{3x}\\ c,=\dfrac{\left(y-x\right)\left(y+x\right)}{xy\left(x-y\right)}=\dfrac{-x-y}{xy}\)

Lời giải:

a.

\(\frac{x^2+xy+x+y}{x^2-xy+x-y}=\frac{x(x+y)+(x+y)}{x(x+1)-y(x+1)}=\frac{(x+y)(x+1)}{(x+1)(x-y)}=\frac{x+y}{x-y}\)

b.

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

c.

\(\frac{y^2-x^2}{x^2y-xy^2}=\frac{(y-x)(y+x)}{-xy(y-x)}=\frac{x+y}{-xy}\)

a: Ta có: \(\left(x-2\right)^2-\left(2x-1\right)^2+\left(3x-1\right)\left(x-5\right)\)

\(=x^2-4x+4-4x^2+4x-1+3x^2-15x-x+5\)

\(=-16x+8\)

b: Ta có: \(\left(x-3\right)^3-\left(x+3\right)\left(x^2-3x+9\right)+\left(3x-1\right)\left(3x+1\right)\)

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

=27x-55

a) \(\left(2a-3\right)\left(a+1\right)-\left(a^2+6a+9\right):\left(a+3\right)\)

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

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

\(=2a^2-a-3-a-3\)

\(=2a^2-2a-6\)

b) \(\left(3x-5y\right)\left(-xy\right)^2-3x^2y^2+4x^2y^3\)

\(=\left(3x-5y\right)\cdot x^2y^2-3x^2y^2+4x^2y^3\)

\(=3x^3y^2-5x^2y^3-3x^2y^2+4x^2y^3\)

\(=3x^3y^2-x^2y^3-3x^2y^2\)

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

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

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

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

\(=4x-8\)

\(a,=x^2-4-x^2-2x-1=-2x-5\\ b,=8x^3-1-8x^3-1=-2\\ 3,\\ a,\Rightarrow x^3+8-x^3+2x=15\\ \Rightarrow2x=7\Rightarrow x=\dfrac{7}{2}\\ b,\Rightarrow x^3-3x^2+3x-1-x^3+3x^2+4x=13\\ \Rightarrow7x=14\Rightarrow x=2\)

Bài 2:

a) \(=x^2-4-x^2-2x-1=-2x-5\)

b) \(=8x^3-1-8x^3-1=-2\)

Bài 3:

a) \(\Rightarrow x^3+8-x^3+2x=15\)

\(\Rightarrow2x=7\Rightarrow x=\dfrac{7}{2}\)

b) \(\Rightarrow x^3-3x^2+3x-1-x^3+3x^2+4x=13\)

\(\Rightarrow7x=14\Rightarrow x=2\)

\(a,=x^2-4-x^2+2x+3=2x-1\\ b,=x^3+3x^2-5x-15+x^2-x^3+4x-4x^2=-x-15\\ c,=2x^2+3x-10x-15-2x^2+6x+x+7=-8\\ d,=\left(2x+1+3x-1\right)^2=25x^2\)

Bạn ơi, làm thế nào mà bạn tính ra được như vậy ạ? Mình thấy nó hơi khó hiểu, bạn có thể ghi rõ ra được không ạ?
Cảm ơn bạn

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

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

\(=7x^2-11x+4\)

Bài 8:

\(F=x^2-2x+1+x^2-6x+9=2x^2-8x+10\\ F=2\left(x^2-4x+4\right)+2=2\left(x-2\right)^2+2\ge2\\ F_{min}=2\Leftrightarrow x=2\)

Bài 9:

\(A=-x^2+2x-1+5=-\left(x-1\right)^2+5\le5\\ A_{max}=5\Leftrightarrow x=1\\ B=-x^2+10x-25+2=-\left(x-5\right)^2+2\le2\\ B_{max}=2\Leftrightarrow x=5\\ C=-x^2+6x-9+9=-\left(x-3\right)^2+9\le9\\ C_{max}=9\Leftrightarrow x=3\)