Solve the formula for f on 26 $$ \frac{1}{a}+\frac{1}{h}=\frac{1}{f} $$

Question

UpStudy AI · Accepted Answer

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 $$ h $$.
$$ f = \frac{a \times h}{a + h} $$

Solve the formula for f on 26 \( \frac{1}{a}+\frac{1}{h}=\frac{1}{f} \)