((a^2+2ab+b^2)/b)×(((a-b)×(a+b))/ab)
You asked:
Evaluate the expression: \(\frac{{a}^{2} + 2 a b + {b}^{2}}{b} \cdot \frac{\left(a - b\right) \cdot \left(a + b\right)}{a b}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{{a}^{2} + 2 a b + {b}^{2}}{b} \cdot \frac{\left(a - b\right) \cdot \left(a + b\right)}{a b} = \frac{\left(a - b\right) \left(a + b\right) \left(a^{2} + 2 a b + b^{2}\right)}{b^{2} a} \)
Expanded
\[\frac{{a}^{2} + 2 a b + {b}^{2}}{b} \cdot \frac{\left(a - b\right) \cdot \left(a + b\right)}{a b} = \frac{a^{3}}{b^{2}} + \frac{2 a^{2}}{b} - 2 b - \frac{b^{2}}{a}\]
Factored
\[\frac{{a}^{2} + 2 a b + {b}^{2}}{b} \cdot \frac{\left(a - b\right) \cdot \left(a + b\right)}{a b} = \frac{\left(a - b\right) \left(a + b\right)^{3}}{b^{2} a}\]