Question

Rút gọn biểu thức sau:

  

Answer 1

\(=\dfrac{3a^2-3ab+ab-b^2}{2a^2+2ab-ab-b^2}:\dfrac{3a^2-3ab-ab+b^2}{3a^2+3ab-ab-b^2}\)

\(=\dfrac{\left(a-b\right)\left(3a+b\right)}{\left(a+b\right)\left(2a-b\right)}\cdot\dfrac{\left(a+b\right)\left(3a-b\right)}{\left(a-b\right)\left(3a-b\right)}\)

\(=\dfrac{\left(3a+b\right)}{2a-b}\)

Answer 2

\(R=\dfrac{3a^2-2ab-b^2}{2a^2+ab-b^2}:\dfrac{3a^2-4ab+b^2}{3a^2+2ab-b^2}\)

\(R=\dfrac{3a^2-3ab+ab-b^2}{2a^2+2ab-ab-b^2}:\dfrac{3a^2-3ab-ab+b^2}{3a^2+3ab-ab-b^2}\)

\(R=\dfrac{\left(3a^2-3ab\right)+\left(ab-b^2\right)}{\left(2a^2+2ab\right)-\left(ab+b^2\right)}:\dfrac{\left(3a^2-3ab\right)-\left(ab-b^2\right)}{\left(3a^2+3ab\right)-\left(ab+b^2\right)}\)

\(R=\dfrac{3a\left(a-b\right)+b\left(a-b\right)}{2a\left(a+b\right)-b\left(a+b\right)}\cdot\dfrac{3a\left(a+b\right)-b\left(a+b\right)}{3a\left(a-b\right)-b\left(a-b\right)}\)

\(R=\dfrac{\left(a-b\right)\left(3a+b\right)}{\left(a+b\right)\left(2a-b\right)}\cdot\dfrac{\left(a+b\right)\left(3a-b\right)}{\left(a-b\right)\left(3a-b\right)}\)

\(R=\dfrac{\left(a-b\right)\left(3a+b\right)}{\left(a+b\right)\left(2a-b\right)}\cdot\dfrac{a+b}{a-b}\)

\(R=\dfrac{3a+b}{2a-b}\)