Question
41. Solve for \( a \) in terms of the other variables: \( \frac{1}{A}=\frac{1}{a}+\frac{1}{b} \)
Ask by Frank Logan. in the United States
Dec 06,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
\( a = \frac{Ab}{b-A} \)
Solution
Solve the equation \( \frac{1}{A}=\frac{1}{a}+\frac{1}{b} \).
Solve the equation by following steps:
- step0: Solve for \(a\):
\(\frac{1}{A}=\frac{1}{a}+\frac{1}{b}\)
- step1: Swap the sides:
\(\frac{1}{a}+\frac{1}{b}=\frac{1}{A}\)
- step2: Move the expression to the right side:
\(\frac{1}{a}=\frac{1}{A}-\frac{1}{b}\)
- step3: Subtract the terms:
\(\frac{1}{a}=\frac{b-A}{Ab}\)
- step4: Rewrite the expression:
\(a=\frac{Ab}{b-A}\)
The solution for \( a \) in terms of the other variables is \( a = \frac{Ab}{b-A} \).
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Simplify this solution Extra Insights
To solve for \( a \) in terms of the other variables given the equation \( \frac{1}{A}=\frac{1}{a}+\frac{1}{b} \), we first isolate the term involving \( a \): 1. Rewrite the equation: \[ \frac{1}{A} = \frac{1}{a} + \frac{1}{b} \] This can be rearranged to: \[ \frac{1}{A} - \frac{1}{b} = \frac{1}{a} \] 2. Finding a common denominator for the left side gives: \[ \frac{b - A}{Ab} = \frac{1}{a} \] 3. Taking the reciprocal of both sides results in: \[ a = \frac{Ab}{b - A} \] So, the solution for \( a \) in terms of \( A \) and \( b \) is: \[ a = \frac{Ab}{b - A} \]
