 To add two fractions, find a common denominator, or remember that multiplying by a number at its inverse leaves the expression unchanged. So if we want to add one-half plus one-third, if we multiply it by six and then by one-sixth, we get the same value, but we can take those multiplications in order. Multiplying the fractional terms by six gives us, and then multiplying the remaining term by one-sixth gives us our final answer. And the important thing to remember here is that rational expressions are the polynomial equivalent of fractions. For example, say we want to add one divided by x minus two plus one divided by x plus three. So remember, you can take small steps. Now notice we have two denominators. Since we have a denominator of x minus two, we can multiply the expression by x minus two and then multiply by its inverse. And since we have a denominator of x plus three, we can multiply the expression by x plus three and then multiply by its inverse. Let's rearrange these factors a little bit. Now we can then distribute this factor, and then we can simplify. With this first expression, we can remove a common factor of x minus two. And in this second expression, we can remove a common factor of x plus three. And then we can simplify. We'll rewrite this as a single fraction. And then remember, factored form is best. We'll leave this in factored form. We can do the same thing if we're subtracting. So if I want to find this difference, we multiply and divide by x times x plus h, the product of the two denominators. Distributing the factor, then removing the common factors, and simplifying gives us our final answer.