This week in Pre Calc 11 we started learning about rational expressions. These were very similar to solving fractional expressions and the rules were very simple as well. I wanted to talk about adding and subtracting in specific. When adding fractions the main rule is that you have to make sure they share a common denominator. When doing this with regular fractions you can easily find one but with rational expressions it can be a little more difficult.
Let’s use this equation as an example. You have to 3 + 2 over two factorable expressions. The first step is to factor these expressions into the simplest form. this gives you (t-2)(t-5) + (t-2)(t-4). Now you can look at what they have in common. Sometimes they won’t have something in common but here they do. That means that each side’s numerator needs to be multiplied by what they don’t have in common. 3 will be multiplied by (t-4) and 2 will be multiplied by (t-5). Now they multiply the denominator by the same numbers so they become common. Your new denominator becomes (t-2)(t-5)(t-4). You only need to write t-2 once as that’s their common factor.
Now, you can simplify the numerators and cancel out anything common in the denominator and numerator. In this example, once you simplify the top, you get t-2, which cancels out with the bottom. In the end, you’ll get 1 over (t-5)(t-4).
that’s your final expression but you’re not done yet. You have to write your non-permissible values. These values are the ones that won’t make the denominator equal to 0. In this case it’s T can’t equal 2,5,4. Always get these values from the original equation as things simplify and cancel out throughout the equation.
That’s how to add/subtract rational expressions.