Question

Hãy tìm đa thức A trong các trường hợp sau: a) x² + 2x / A = x / 3 với x không bằng 0 b) A/ 3x -2 = 15x² + 10x / 9x² -4

Answer 1

a) \(\dfrac{x^2+2x}{A}=\dfrac{x}{3}\)

\(\Rightarrow A=\dfrac{\left(x^2+2x\right)\cdot3}{x}\)

\(\Rightarrow A=\dfrac{x\left(x+2\right)\cdot3}{x}\)

\(\Rightarrow A=3x+6\)

b) \(\dfrac{A}{3x-2}=\dfrac{15x^2+10x}{9x^2-4}\)

\(\Rightarrow A=\dfrac{\left(3x-2\right)\left(15x^2+10x\right)}{9x^2-4}\)

\(\Rightarrow A=\dfrac{5x\left(3x-2\right)\left(3x+2\right)}{\left(3x\right)^2-2^2}\)

\(\Rightarrow A=\dfrac{5x\left(3x+2\right)\left(3x-2\right)}{\left(3x+2\right)\left(3x-2\right)}\)

\(\Rightarrow A=5x\)