Question
Solve the formula for f on 26 \( \frac{1}{a}+\frac{1}{h}=\frac{1}{f} \)
Ask by Gibson Potter. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f = \frac{a \times h}{a + h} \)
Solution
To solve the equation
\[
\frac{1}{a} + \frac{1}{h} = \frac{1}{f}
\]
for \( f \), follow these steps:
1. **Combine the Fractions on the Left Side:**
\[
\frac{1}{a} + \frac{1}{h} = \frac{h + a}{a h}
\]
So the equation becomes:
\[
\frac{h + a}{a h} = \frac{1}{f}
\]
2. **Take the Reciprocal of Both Sides to Solve for \( f \):**
\[
f = \frac{a h}{h + a}
\]
3. **Simplify the Expression (Optional):**
You can also write the equation as:
\[
f = \frac{a \times h}{a + h}
\]
Or, if preferred:
\[
f = \frac{ah}{a + h}
\]
**Final Solution:**
\[
f = \frac{a \times h}{a + h}
\]
This formula shows that \( f \) is the harmonic mean of \( a \) and \( h \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve for \( f \) in the equation \( \frac{1}{a} + \frac{1}{h} = \frac{1}{f} \), we first combine the fractions on the left side: 1. Find a common denominator, which is \( ah \): \[ \frac{h}{ah} + \frac{a}{ah} = \frac{h + a}{ah} \] 2. Now the equation looks like this: \[ \frac{h + a}{ah} = \frac{1}{f} \] 3. To isolate \( f \), take the reciprocal of both sides: \[ f = \frac{ah}{h + a} \] And there you have it! The formula solved for \( f \) is: \[ f = \frac{ah}{h + a} \]
