a) Đa thức A là:
\(\dfrac{-2x+4}{x-2}=\dfrac{2}{A}\)
\(\Leftrightarrow\dfrac{-2\left(x-2\right)}{x-2}=\dfrac{2}{A}\)
\(\Leftrightarrow-2=\dfrac{2}{A}\)
\(\Leftrightarrow A=\dfrac{2}{-2}=-1\)
b) Đa thức A là:
\(\dfrac{2x^2+4x}{x+2}=\dfrac{A}{2}\)
\(\Leftrightarrow\dfrac{2x\left(x+2\right)}{x+2}=\dfrac{A}{2}\)
\(\Leftrightarrow2x=\dfrac{A}{2}\)
\(\Leftrightarrow A=2x\cdot2=4x\)
c) Đa thức A là:
\(\dfrac{x-4}{x^2-16}=\dfrac{1}{A}\)
\(\Leftrightarrow\dfrac{x-4}{\left(x+4\right)\left(x-4\right)}=\dfrac{1}{A}\)
\(\Leftrightarrow\dfrac{1}{x+4}=\dfrac{1}{A}\)
\(\Leftrightarrow A=x+4\)
d) Đa thức A là:
\(\dfrac{x^3+8}{x+2}=\dfrac{A}{2}\)
\(\Leftrightarrow\dfrac{\left(x+2\right)\left(x^2+2x+4\right)}{x+2}=\dfrac{A}{2}\)
\(\Leftrightarrow x^2+2x+4=\dfrac{A}{2}\)
\(\Leftrightarrow A=2\cdot\left(x^2+2x+4\right)=2x^2+4x+8\)
a: 2/A=-2x+4/x-2
=>2/A=-2
=>A=-1
b: 2x^2+4x/x+2=A/2
=>A/2=2x
=>A=4x
c: (x-4)/(x^2-16)=1/A
=>1/A=1/x+4
=>A=x+4
d: (x^3+8)/(x+2)=A/2
=>A/2=x^2-2x+4
=>A=2x^2-4x+8
