Math Problem Solver

Simplified:

$$\frac{\frac{\frac{8 {x}^{3} - 1}{4 {x}^{3} + 2 {x}^{2}}}{\frac{6 {x}^{2} - 13 x + 5}{15 x - 25}} \left(2 {x}^{4} + {x}^{3}\right)}{15 {x}^{3}} = \frac{4 x^{2} + 2 x + 1}{6 x^{2}}$$

$$\begin{aligned}\frac{\left(8 x^{3} - 1\right) \left(2 x^{4} + x^{3}\right)}{\frac{6 x^{2} - 13 x + 5}{15 x - 25} \cdot \left(4 x^{3} + 2 x^{2}\right) 15 x^{3}}&=\frac{\left(15 x - 25\right) \left(8 x^{3} - 1\right) \left(2 x^{4} + x^{3}\right)}{15 x^{3} \cdot \left(6 x^{2} - 13 x + 5\right) \left(4 x^{3} + 2 x^{2}\right)}\\&=\frac{4 x^{2} + 2 x + 1}{6 x^{2}}\end{aligned}$$

Expanded:

$$\frac{\frac{\frac{8 {x}^{3} - 1}{4 {x}^{3} + 2 {x}^{2}}}{\frac{6 {x}^{2} - 13 x + 5}{15 x - 25}} \left(2 {x}^{4} + {x}^{3}\right)}{15 {x}^{3}} = \frac{16 x^{4}}{\frac{360 x^{5}}{15 x - 25} - \frac{600 x^{4}}{15 x - 25} - \frac{90 x^{3}}{15 x - 25} + \frac{150 x^{2}}{15 x - 25}} + \frac{8 x^{3}}{\frac{360 x^{5}}{15 x - 25} - \frac{600 x^{4}}{15 x - 25} - \frac{90 x^{3}}{15 x - 25} + \frac{150 x^{2}}{15 x - 25}} - \frac{2 x}{\frac{360 x^{5}}{15 x - 25} - \frac{600 x^{4}}{15 x - 25} - \frac{90 x^{3}}{15 x - 25} + \frac{150 x^{2}}{15 x - 25}} - \frac{1}{\frac{360 x^{5}}{15 x - 25} - \frac{600 x^{4}}{15 x - 25} - \frac{90 x^{3}}{15 x - 25} + \frac{150 x^{2}}{15 x - 25}}$$

Factored:

$$\frac{\frac{\frac{8 {x}^{3} - 1}{4 {x}^{3} + 2 {x}^{2}}}{\frac{6 {x}^{2} - 13 x + 5}{15 x - 25}} \left(2 {x}^{4} + {x}^{3}\right)}{15 {x}^{3}} = \frac{4 x^{2} + 2 x + 1}{6 x^{2}}$$