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a: \(A=\dfrac{2\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}=\dfrac{2}{x-2}\)
b: \(B=\dfrac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)^2}=\dfrac{x+3}{x-3}\)
c: \(C=\dfrac{\left(3x-4\right)\left(3x+4\right)}{x\left(3x-4\right)}=\dfrac{3x+4}{x}\)
d: \(D=\dfrac{\left(x+2\right)^2}{2\left(x+2\right)}=\dfrac{x+2}{2}\)
e: \(E=\dfrac{-x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{-x}{x+2}\)
f: \(F=\dfrac{3\left(x^2+2x+4\right)}{\left(x-2\right)\left(x^2+2x+4\right)}=\dfrac{3}{x-2}\)
(3x+2)(2x+9)-(x+2)(6x+1)=(x+1)-(x-6)
6x^2+27x+4x+18-6x^2-x-12x-2=x+1-x+6
18x+16=7
18x=7-16
x=-9/18=-2
vậy x =-2
(3x+2)(2x+9)-(x+2)(6x+1)=(x+1)-(x-6)
<=>(6x2+27x+4x+18)-(6x2+x+12x+2)=x+1-x+6
<=>6x2+31x+18-6x2-13x-2=7
<=>18x+16=7
<=>18x=-9
<=>x=-1/2
7)(16-8x)(2-6x)=0
=> 16 - 8x = 0 hoặc 2 - 6x = 0
=> 16 = 8x hoặc 2 = 6x
=> x = 2 hoặc x = 1/3
8) (x+4)(6x-12)=0
=> x + 4 = 0 hoặc 6x - 12 = 0
=> x = -4 hoặc x = 2
9) (11-33x)(x+11)=0
=> 11 - 33x = 0 hoặc x + 11 = 0
=> x = 1/3 hoặc x = -11
10) (x-1/4)(x+5/6)=0
=> x - 1/4 = 0 hoặc x + 5/6 = 0
=> x = 1/4 hoặc x = -5/6
11) (7/8-2x)(3x+1/3)=0
=> 7/8 - 2x = 0 hoặc 3x + 1/3 = 0
=> 2x = 7/8 hoặc 3x = -1/3
=> x = 7/16 hoặc x = -1/9
12)3x-2x^2=0
=> x(3 - 2x) = 0
=> x = 0 hoặc 3 - 2x = 0
=> x = 0 hoặc x = 3/2
\(a,\left(16-8x\right)\left(2-6x\right)=0\)
\(\hept{\begin{cases}16-8x=0\\2-6x=0\end{cases}\Rightarrow\hept{\begin{cases}x=2\\x=\frac{1}{3}\end{cases}}}\)
\(b,\left(x+4\right)\left(6x-12\right)=0\)
\(\hept{\begin{cases}x+4=0\\6x-12=0\end{cases}\Rightarrow\hept{\begin{cases}x=-4\\x=2\end{cases}}}\)
\(c,\left(11-33x\right)\left(x+11\right)=0\)
\(\hept{\begin{cases}11-33x=0\\x+11=0\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{1}{3}\\x=-11\end{cases}}}\)
\(d,\left(x-\frac{1}{4}\right)\left(x+\frac{5}{6}\right)=0\)
\(\hept{\begin{cases}x-\frac{1}{4}=0\\x+\frac{5}{6}=0\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{1}{4}\\x=-\frac{5}{6}\end{cases}}}\)
\(e,\left(\frac{7}{8}-2x\right)\left(3x+\frac{1}{3}\right)=0\)
\(\hept{\begin{cases}\frac{7}{x}-2x=0\\3x+\frac{1}{3}=0\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{7}{4}\\x=-\frac{1}{9}\end{cases}}}\)
\(f,3x-2x^2=0\)
\(x\left(3-2x\right)=0\)
\(\hept{\begin{cases}x=0\\3-2x=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\x=\frac{3}{2}\end{cases}}}\)