a: \(=\dfrac{5\left(x+2\right)}{10xy^2}\cdot\dfrac{12x}{x+2}=\dfrac{60x}{10xy^2}=\dfrac{6}{y^2}\)

b: \(=\dfrac{x-4}{3x-1}\cdot\dfrac{3\left(3x-1\right)}{\left(x-4\right)\left(x+4\right)}=\dfrac{3}{x+4}\)

c: \(=\dfrac{2\left(2x+1\right)}{\left(x+4\right)^2}\cdot\dfrac{\left(x+4\right)}{3\left(x+3\right)}=\dfrac{2\left(2x+1\right)}{3\left(x+3\right)\left(x+4\right)}\)

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

Câu 3: 

a: 2x-8=4

nên 2x=12

hay x=6

b: 7x-3x=2x+7

\(\Leftrightarrow4x-2x=7\)

hay \(x=\dfrac{7}{2}\)

Câu 1:

a: \(5x\left(3x-4\right)=15x^2-20x\)

b: \(\left(x+5\right)\left(x-5\right)=x^2-25\)

c) \(5x^2.\left(3x^2-7x+2\right)\)

\(=5x^2.3x^2-5x^2.7x+5x^2.2\)

\(=15x^4-35x^3+10x^2\)

d) \(\dfrac{3x^2y^2+6x^2y^3-12xy}{3xy}\)

\(=\dfrac{3xy\left(xy+2y-4\right)}{3xy}\)

\(=xy+2y-4\)

tách nhỏ câu hỏi ra

1. -3(-x+3)

= 3x - 6

2. -5x³ (-3x + 5)

= 15x⁴ - 25x³

3. -2x (-2x - 6)

= 4x² + 12x

a: \(=\dfrac{2x^4+x^3-5x^2-3x-3}{x^2-3}\)

\(=\dfrac{2x^4-6x^2+x^3-3x+x^2-3}{x^2-3}\)

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

b: \(=\dfrac{x^5+x^2+x^3+1}{x^3+1}=x^2+1\)

c: \(=\dfrac{2x^3-x^2-x+6x^2-3x-3+2x+6}{2x^2-x-1}\)

\(=x+3+\dfrac{2x+6}{2x^2-x-1}\)

d: \(=\dfrac{3x^4-8x^3-10x^2+8x-5}{3x^2-2x+1}\)

\(=\dfrac{3x^4-2x^3+x^2-6x^3+4x^2-2x-15x^2+10x-5}{3x^2-2x+1}\)

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

Bài 1:

\(a,4x\left(5x^2-2x+3\right)=20x^3-8x^2+12x\\ b,\left(x-2\right)\left(x^2-3x+5\right)=x^3-2x^2-3x^2+6x+5x-10=x^3-5x^2+11x-10\)

Bài 5:

\(P_{\left(x\right)}=-x^2+13x+2019\\ =-(x^2-13x+\left(\dfrac{13}{2}\right)^2)+2019+\dfrac{169}{4}\\ =-\left(x-\dfrac{13}{2}\right)^2+2061,25\\ Tacó:-\left(x-\dfrac{13}{2}\right)^2\le0\forall x\\ \Rightarrow P_{\left(x\right)}\le2061,25\\ \Rightarrow Max_P=2061,25\Leftrightarrow\left(x-\dfrac{13}{2}\right)^2=0\\ \Leftrightarrow x=\dfrac{13}{2}\)

Bài 3:

a: \(=x\left(x+5\right)+5y\left(x+5\right)=\left(x+5\right)\left(x+5y\right)\)

b: \(=\left(x+7\right)^2-y^2=\left(x+7+y\right)\left(x+7-y\right)\)

c: \(=x^2-25x+x-25=\left(x-25\right)\left(x+1\right)\)

b) \(\dfrac{x}{x-3}\) + \(\dfrac{-9}{x^2-3x}\)

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

=\(\dfrac{x.x}{x\left(x-3\right)}\) + \(\dfrac{-9}{x\left(x-3\right)}\)

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

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

=\(\dfrac{x+3}{x}\)

#Fiona

c) \(\dfrac{3}{x-3}-\dfrac{6x}{9-x^2}+\dfrac{x}{x+3}\)

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

=\(\dfrac{3}{x-3}\)+\(\dfrac{6x}{\left(x+3\right)\left(x-3\right)}\)+\(\dfrac{x}{x+3}\)

=\(\dfrac{3\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)+\(\dfrac{6x}{\left(x+3\right)\left(x-3\right)}\)+\(\dfrac{x\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}\)

=\(\dfrac{3x+9+6x+x^2-3x}{\left(x-3\right)\left(x+3\right)}\)

=\(\dfrac{9+6x+x^2}{\left(x-3\right)\left(x+3\right)}\)

=\(\dfrac{3^2+2.3x+x^2}{\left(x-3\right)\left(x+3\right)}\)

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

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

=\(\dfrac{x-3}{x+3}\)

#Fiona 

Tick đúng giúp mình nhaa<3

d)\(\dfrac{5x+10}{4x-8}\).\(\dfrac{x-2}{x+2}\)

=\(\dfrac{5\left(x+2\right)}{4\left(x-2\right)}\) . \(\dfrac{x-2}{x+2}\)

=\(\dfrac{5\left(x+2\right).\left(x-2\right)\text{​​}\text{​​}}{4\left(x-2\right).\left(x+2\right)}\)

=\(\dfrac{5}{4}\)

#Fiona

Tick đúng giúp mikk nhaa