The equation you're working with is:

\[
\frac{1}{x} + \frac{1}{y} = \frac{1}{110}
\]

We need to express \(x + y\) in terms of a known value. Here's the step-by-step solution:

### Step 1: Combine the terms on the left-hand side
We first rewrite the left-hand side of the equation as a single fraction:

\[
\frac{x + y}{xy} = \frac{1}{110}
\]

### Step 2: Cross-multiply
Next, cross-multiply to eliminate the fractions:

\[
110(x + y) = xy
\]

### Step 3: Rearrange the equation
Rearranging the terms gives:

\[
xy - 110(x + y) = 0
\]

This equation gives a relationship between \(x + y\) and \(xy\), but the value of \(x + y\) cannot be uniquely determined from this equation alone. You'd need additional information, like the value of either \(x\) or \(y\), to solve this completely.

Would you like more details on how to proceed, or do you have a specific value for one of the variables?

### Related Questions:
1. What would happen if \( x = y \) in this equation?
2. How can we use the quadratic equation to solve for \(x\) and \(y\)?
3. Can we solve this equation for specific values of \(x\) and \(y\)?
4. How would this equation change if we modified the constant \(110\) on the right-hand side?
5. How would you graphically represent this equation in terms of \(x\) and \(y\)?

### Tip:
When dealing with reciprocal equations like this, finding a common denominator is key to simplifying the problem.

Explore how to solve the reciprocal equation 1/x + 1/y = 1/110, including the key algebraic concepts of combining fractions and cross-multiplying. This problem is suitable for students in Grades 9-11 and involves expressing x + y in terms of known values.

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