Question

tìm đa thức A biết A/2x-1=6x³+3x²/4x²-1

Answer 1

\(\dfrac{A}{2x-1}=\dfrac{6x^3+3x^2}{4x^2-1}\Leftrightarrow\dfrac{A}{2x-1}=\dfrac{3x^2\left(2x+1\right)}{\left(2x-1\right)\left(2x+1\right)}\Leftrightarrow\dfrac{A}{2x-1}=\dfrac{3x^2}{2x-1}\Leftrightarrow A=3x^2\)

Answer 2

Ta có: \(\dfrac{A}{2x-1}=\dfrac{6x^3+3x^2}{4x^2-1}\)

\(\Leftrightarrow\dfrac{A}{2x-1}=\dfrac{3x^2\left(2x+1\right)}{\left(2x+1\right)\left(2x-1\right)}\)

\(\Leftrightarrow\dfrac{A}{2x-1}=\dfrac{3x^2}{2x-1}\)

hay \(A=3x^2\)