$\frac{3v-1}{7v^2-58-45}$ / $\frac{3v-1}{7^2-2v-5}$

asked by guest
on Sep 24, 2024 at 1:29 pm



You asked:

Evaluate the expression: \(\frac{\frac{3 v - 1}{7 \cdot {v}^{2} - 58 - 45}}{\frac{3 v - 1}{{7}^{2} - 2 v - 5}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\frac{3 v - 1}{7 \cdot {v}^{2} - 58 - 45}}{\frac{3 v - 1}{{7}^{2} - 2 v - 5}} = \frac{44 - 2 v}{7 v^{2} - 103} \)

Expanded

\[\frac{\frac{3 v - 1}{7 \cdot {v}^{2} - 58 - 45}}{\frac{3 v - 1}{{7}^{2} - 2 v - 5}} = \frac{3 v}{\frac{21 v^{3}}{44 - 2 v} - \frac{7 v^{2}}{44 - 2 v} - \frac{309 v}{44 - 2 v} + \frac{103}{44 - 2 v}} - \frac{1}{\frac{21 v^{3}}{44 - 2 v} - \frac{7 v^{2}}{44 - 2 v} - \frac{309 v}{44 - 2 v} + \frac{103}{44 - 2 v}}\]

Factored

\[\frac{\frac{3 v - 1}{7 \cdot {v}^{2} - 58 - 45}}{\frac{3 v - 1}{{7}^{2} - 2 v - 5}} = - \frac{2 \left(v - 22\right)}{7 v^{2} - 103}\]

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