(2b/a)/(b^3-2ab^2/4a^3-2a^2b)
You asked:
Evaluate the expression: \(\frac{\frac{2 b}{a}}{{b}^{3} - \frac{2 a \cdot {b}^{2}}{4 \cdot {a}^{3}} - 2 \cdot {a}^{2} \cdot b}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{\frac{2 b}{a}}{{b}^{3} - \frac{2 a \cdot {b}^{2}}{4 \cdot {a}^{3}} - 2 \cdot {a}^{2} \cdot b} = \frac{2 b}{a \left(- 2 a^{2} b + b^{3} - \frac{b^{2}}{2 a^{2}}\right)} \)
Expanded
\[\frac{\frac{2 b}{a}}{{b}^{3} - \frac{2 a \cdot {b}^{2}}{4 \cdot {a}^{3}} - 2 \cdot {a}^{2} \cdot b} = \frac{2 b}{- 2 a^{3} b + b^{3} a - \frac{b^{2}}{2 a}}\]
Factored
\[\frac{\frac{2 b}{a}}{{b}^{3} - \frac{2 a \cdot {b}^{2}}{4 \cdot {a}^{3}} - 2 \cdot {a}^{2} \cdot b} = - \frac{4 a}{4 a^{4} - 2 a^{2} b^{2} + b}\]