Question

Evaluate the following when $a = 3$, $b = \frac14$, and $c = 5$: \[ \frac{b^{-1}}{ca^{-1} - ac^{-1}}. \] Thank you so much!

Answer 1

$\dfrac{b^{-1}}{ca^{-1}-ac^{-1}}=\dfrac{\frac1b}{\frac ca-\frac ac}$

Multiply the numerator and denominator by $ac$:

$\dfrac{\frac1b}{\frac ca-\frac ac}\cdot\dfrac{ac}{ac}=\dfrac{\frac{ac}b}{c-a}$

Since $b=\frac14$, we have $b^{-1}=\frac1b=4$. So substituting the values of a, b, and c gives us

$\dfrac{\frac{ac}b}{c-a}=\dfrac{3\cdot5\cdot4}{5-3}=\dfrac{60}2=\boxed{30}$

Answer 2

Answer:

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Step-by-step explanation: