Simplify (8x ^ 3 - 1)/(4x ^ 3 + 2x ^ 2) / ((6x ^ 2 - 13x + 5)/(15x - 25)) * (2x ^ 4 + x ^ 3)/(15x ^ 3)

asked by guest
on Dec 07, 2024 at 11:07 pm



You asked:

Simplify the expression: \(\frac{\frac{\frac{8 {x}^{3} - 1}{4 {x}^{3} + 2 {x}^{2}}}{\frac{6 {x}^{2} - 13 x + 5}{15 x - 25}} \left(2 {x}^{4} + {x}^{3}\right)}{15 {x}^{3}}\)

MathBot Answer:

Simplified:

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

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:

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


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