$\frac{3v-1}{7v^2-58-45}$ / $\frac{3v-1}{7^2-58-45}$

asked by guest
on Sep 24, 2024 at 1:28 pm



You asked:

Evaluate the expression: \(\frac{\frac{3 v - 1}{7 \cdot {v}^{2} - 58 - 45}}{\frac{3 v - 1}{{7}^{2} - 58 - 45}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\frac{3 v - 1}{7 \cdot {v}^{2} - 58 - 45}}{\frac{3 v - 1}{{7}^{2} - 58 - 45}} = \frac{3 v - 1}{\left(\frac{1}{54} - \frac{v}{18}\right) \left(7 v^{2} - 103\right)} \)

Expanded

\[\frac{\frac{3 v - 1}{7 \cdot {v}^{2} - 58 - 45}}{\frac{3 v - 1}{{7}^{2} - 58 - 45}} = \frac{3 v}{- \frac{7 v^{3}}{18} + \frac{7 v^{2}}{54} + \frac{103 v}{18} - \frac{103}{54}} - \frac{1}{- \frac{7 v^{3}}{18} + \frac{7 v^{2}}{54} + \frac{103 v}{18} - \frac{103}{54}}\]

Factored

\[\frac{\frac{3 v - 1}{7 \cdot {v}^{2} - 58 - 45}}{\frac{3 v - 1}{{7}^{2} - 58 - 45}} = - \frac{54}{7 v^{2} - 103}\]

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