(10x-5y /48xy^2) / (4x^2-y^2 /16x^3y)
You asked:
Evaluate the expression: \(\frac{10 x - \frac{5 y}{48 x \cdot {y}^{2}}}{4 \cdot {x}^{2} - \frac{{y}^{2}}{16 \cdot {x}^{3} \cdot y}}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{10 x - \frac{5 y}{48 x \cdot {y}^{2}}}{4 \cdot {x}^{2} - \frac{{y}^{2}}{16 \cdot {x}^{3} \cdot y}} = \frac{10 x - \frac{5}{48 x y}}{4 x^{2} - \frac{y}{16 x^{3}}} \)
Expanded
\[\frac{10 x - \frac{5 y}{48 x \cdot {y}^{2}}}{4 \cdot {x}^{2} - \frac{{y}^{2}}{16 \cdot {x}^{3} \cdot y}} = \frac{10 x}{4 x^{2} - \frac{y}{16 x^{3}}} - \frac{5}{192 x^{3} y - \frac{3 y^{2}}{x^{2}}}\]
Factored
\[\frac{10 x - \frac{5 y}{48 x \cdot {y}^{2}}}{4 \cdot {x}^{2} - \frac{{y}^{2}}{16 \cdot {x}^{3} \cdot y}} = \frac{5 x^{2} \cdot \left(96 x^{2} y - 1\right)}{3 y \left(64 x^{5} - y\right)}\]