Add or subtract, as indicated. See Example 4.

3 1
——— - ———
a ...

Question

Add or subtract, as indicated. See Example 4.

3 1
——— - ———
 a - 2 2 - a

Accepted Answer

Welcome back. Everyone in this problem, we want to simplify the radic, the rational expression of nine divided by the expression D minus 13 minus four divided by the expression 13 minus D. For our answer choices, A is five divided by the expression D minus 13, B is 13 divided by the same expression C is 65 divided by the same expression. And the D is 169 divided by the same expression. Now, what are we trying to figure out here? Well, we want to simplify our rational expression and let me rewrite it here a little clearer for everyone to see. Now, look at both of these expressions. Do you notice anything in common? Well, do you notice that the denominator for first expression D minus 13 is the additive inverse of the denominator for a second expression 13 minus D, remember that if we're going to simplify fractions, we want their denominators to be alike. So if we can figure out a way to make both of those denominators the same, then we can go ahead and combine our numerators. Now, one way we can do that is by multiplying our, one of the expressions by negative one. Because if we multiply our denominator in the second expression by negative one, it will become D minus 13. Likewise, we'll have to multiply our numerator by a negative one to keep the value of the expression the same. So let's go ahead and do that. So our first expression remains D divided by sorry nine, divided by D minus 13. But in our second expression, we'll have four multiplied by negative one, which is negative four and we have 13 minus D multiplied by a negative 1, 13 multiplied by a negative one is negative 13 and A negative D multiplied by a negative one is a positive. D know that both of the denominators are the same. We can combine the numerators. So that would be nine minus negative four. But when we subtract the negative, it becomes positive. So we can actually write it as nine plus four divided by D minus 13 and the nine plus four is 13. Therefore, our final answer is 13 divided by the expression D minus 13. And when you look in our answer choices, that would have been answer choice. B thanks a lot for watching everyone. I hope this video helped.

Add or subtract, as indicated. See Example 4. 3 1 ——— - ——— a - 2 2 - a

Key Concepts

Rational Expressions

Common Denominator

Factoring Polynomials

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