The image contains a mathematical expression that involves the simplification of a difference of two fractions. The expression is:

$\frac{1}{(x+h)-5} - \frac{1}{x-5}$

This expression is over the denominator $h$. To simplify this, follow these steps:

Step 1: Find a common denominator

The denominators are $(x+h)-5$ and $x-5$. The common denominator will be the product of these two terms: $(x+h-5)(x-5)$

Step 2: Rewriting the terms

We rewrite each fraction with the common denominator:

$\frac{1}{(x+h-5)} = \frac{(x-5)}{(x+h-5)(x-5)}$ $\frac{1}{(x-5)} = \frac{(x+h-5)}{(x+h-5)(x-5)}$

Step 3: Subtract the fractions

Now subtract the two fractions:

$\frac{(x-5)}{(x+h-5)(x-5)} - \frac{(x+h-5)}{(x+h-5)(x-5)}$

Since the denominators are the same, subtract the numerators:

$\frac{(x-5) - (x+h-5)}{(x+h-5)(x-5)}$

Step 4: Simplify the numerator

Simplify the numerator:

$(x-5) - (x+h-5) = x - 5 - x - h + 5 = -h$

Thus, the expression becomes:

$\frac{-h}{(x+h-5)(x-5)}$

Step 5: Final simplification

The entire expression is divided by $h$, so we get:

$\frac{-h}{h(x+h-5)(x-5)} = \frac{-1}{(x+h-5)(x-5)}$

Final simplified expression:

$\frac{-1}{(x+h-5)(x-5)}$

Let me know if you would like further details or have any questions!

Here are some related questions to explore:

1. How do you simplify rational expressions with different denominators?
2. How would you approach simplifying expressions with polynomials in the numerator and denominator?
3. Can you explain how to combine fractions using the least common denominator?
4. How would the result change if you had to evaluate this expression for specific values of $x$ and $h$?
5. How does this process relate to finding the derivative of a function using limits?

Tip: Always factor any terms when simplifying rational expressions to avoid missing opportunities to cancel common factors.