Add or subtract, as indicated. See Example 4. x + y 2x——— - ——— 2...

Question

Add or subtract, as indicated. See Example 4. x + y 2x——— - ——— 2x - y y - 2x

Accepted Answer

Welcome back. Everyone. In this problem, we want to simplify the rational expression, A plus B divided by the expression eight A minus seven B minus seven B divided by the expression seven B minus eight A. For our answer choices A is one, B is A minus B all divided by the expression eight A minus seven BC is A plus eight B all divided by the expression eight A minus seven B and D is eight A plus seven B all divided by the expression eight A minus seven B. Now, what do we know here? Well, we are trying to simplify our rational expression and here we have two cautions again, A plus B all divided by the expression eight A minus seven B minus seven B all divided by the expression seven B minus eight A. Now you will also notice that the expression in the denominator eight A minus seven B of our first quotient is the additive inverse of the denominator in the second expression, seven B minus eight A. In other words, one is the opposite of the other. So if we're going to simplify and combine these terms into one in the same way that we try to find like denominators for regular fractions. If we can make these denominators alike, then it's easier for us to simplify. And we can do that because we can change the value of one of our expressions or we can make it its own additive inverse when we multiply the entire caution by a negative one. So if we go ahead and do that, OK. So let's say we're multiplying seven B all divided by the expression on seven B minus eight A by a negative one. It means we're going to multiply both of them by negative one, both the numerator and the denominator. So when we go ahead and do that, we still have the same value for the first. But for the second, no, seven B multiplied by negative one. That's negative seven B and seven B minus eight A multiplied by a negative one is going to be a negative seven B and A positive eight A. No, both terms have the same denominator. So we can go ahead and combine our enumerators. So that means no, we're going to have A plus B minus negative seven B which is going to turn into a positive seven B. And all of that is going to be divided by eight A minus seven B A plus B plus seven B that equals A plus eight B. And all of that will be divided by the expression eight A minus seven B when we look in our answer choices that would have been answer choice. C thanks a lot for watching everyone. I hope this video helped.

Add or subtract, as indicated. See Example 4. x + y 2x——— - ——— 2x - y y - 2x

Key Concepts

Rational Expressions

Common Denominator

Simplifying Expressions

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