(10x-5y)/(48xy^2) รท (4x^2-y^2)/(16x^3y)
You asked:
Evaluate the expression: \(\frac{\frac{\frac{10 x - 5 y}{48 x \cdot {y}^{2}}}{4 \cdot {x}^{2} - {y}^{2}}}{16 \cdot {x}^{3} \cdot y}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{\frac{\frac{10 x - 5 y}{48 x \cdot {y}^{2}}}{4 \cdot {x}^{2} - {y}^{2}}}{16 \cdot {x}^{3} \cdot y} = \frac{10 x - 5 y}{768 x^{4} y^{3} \cdot \left(4 x^{2} - y^{2}\right)} \)
Expanded
\[\frac{\frac{\frac{10 x - 5 y}{48 x \cdot {y}^{2}}}{4 \cdot {x}^{2} - {y}^{2}}}{16 \cdot {x}^{3} \cdot y} = - \frac{5}{3072 x^{6} y^{2} - 768 x^{4} y^{4}} + \frac{5}{1536 x^{5} y^{3} - 384 x^{3} y^{5}}\]
Factored
\[\frac{\frac{\frac{10 x - 5 y}{48 x \cdot {y}^{2}}}{4 \cdot {x}^{2} - {y}^{2}}}{16 \cdot {x}^{3} \cdot y} = \frac{5}{768 x^{4} y^{3} \cdot \left(2 x + y\right)}\]