Điều kiện: $a\ne 0, b\ne 0, a\ne b$
$A=\dfrac{2a^2+3ab+b^2}{a^2-2ab+b^2}$
Chia cả tử và mẫu cho $a^2$:
$A=\dfrac{\dfrac{2a^2}{a^2}+\dfrac{3ab}{a^2}+\dfrac{b^2}{a^2}}{\dfrac{a^2}{a^2}-\dfrac{2ab}{a^2}+\dfrac{b^2}{b^2}}$
$=\dfrac{2+3.\dfrac{b}{a}+\Big(\dfrac{b}{a}\Big)^2}{1-2.\dfrac{b}{a}+\Big(\dfrac{b}{a}\Big)^2}$
$=\dfrac{2+3.\dfrac{2}{3}+\dfrac{4}{9}}{1-2.\dfrac{2}{3}+\dfrac{4}{9}}$
$=40$
