a) \(\dfrac{x^2-2x-8}{2x^2-8}=\dfrac{x-4}{A}\)
\(\Leftrightarrow A=\dfrac{\left(2x^2-8\right)\left(x-4\right)}{x^2-2x-8}\)
\(\Leftrightarrow A=\dfrac{2\left(x^2-4\right)\left(x-4\right)}{\left(x-4\right)\left(x+2\right)}\)
\(\Leftrightarrow A=\dfrac{2\left(x+2\right)\left(x-2\right)\left(x-4\right)}{\left(x-4\right)\left(x+2\right)}\)
\(\Leftrightarrow A=2x-4\)
b) \(\dfrac{A}{7x^2+9x+2}=\dfrac{4x-3}{7x+2}\)
\(\Leftrightarrow A=\dfrac{\left(4x-3\right)\left(7x^2+9x+2\right)}{7x+2}\)
\(\Leftrightarrow A=\dfrac{\left(4x-3\right)\left(x+1\right)\left(7x+2\right)}{7x+2}\)
\(\Leftrightarrow A=\left(4x-3\right)\left(x+1\right)\)
\(\Leftrightarrow A=4x^2+x-3\)
c) \(\dfrac{2x^2-5x-12}{A}=\dfrac{x^2+7x+6}{x+1}\)
\(\Leftrightarrow A=\dfrac{\left(2x^2-5x-12\right)\left(x+1\right)}{x^2+7x+6}\)
\(\Leftrightarrow A=\dfrac{\left(x-4\right)\left(2x+3\right)\left(x+1\right)}{\left(x+1\right)\left(x+6\right)}\)
\(\Leftrightarrow A=\dfrac{\left(x-4\right)\left(2x+3\right)}{x+6}\)
\(\Leftrightarrow A=\dfrac{2x^2-5x-12}{x+6}\)
d) \(\dfrac{2x^2-3x+1}{2x-1}=\dfrac{A}{x+3}\)
\(\Leftrightarrow A=\dfrac{\left(x+3\right)\left(2x^2-3x+1\right)}{2x-1}\)
\(\Leftrightarrow A=\dfrac{\left(x+3\right)\left(x-1\right)\left(2x-1\right)}{2x-1}\)
\(\Leftrightarrow A=\left(x+3\right)\left(x-1\right)\)
\(\Leftrightarrow A=x^2+2x-3\)
a) \(\dfrac{x^2-2x-8}{2x^2-8}=\dfrac{x-4}{A}\)
\(\Leftrightarrow A=\dfrac{\left(2x^2-8\right)\left(x-4\right)}{x^2-2x-8}\)
\(\Leftrightarrow A=\dfrac{2x^3-8x^2-8x+32}{x^2-2x-8}\)
Sau khi chia đa thức ta được
\(\Leftrightarrow A=2x-4\)
