Add or subtract, as indicated. See Example 4. ((17y + 3)/(9y +...

Question

Add or subtract, as indicated. See Example 4. ((17y + 3)/(9y + 7)) - ((-10y - 18)/(9y + 7 ))

Accepted Answer

Welcome back. Everyone in this problem. We want to simplify the rational expression. 19 R plus nine all divided by the expression 13 R plus four minus negative 33 R minus seven, all divided by the expression 13 R plus four. For our answer choices A is 13, RB is 54 R plus 16, C is zero and D is four. Now, if we are going to simplify our expression and we are dealing with two cautions here, two fractions, we can just go ahead and combine them. And that's because the denominators for both fractions are the same. So that means we can rewrite it by combining the numerator 19 R plus nine minus negative 33 R minus seven. And we're going to be dividing all of that by 13 R plus four, no, 19 R plus 19. We can sorry 19 R plus nine, we can rewrite that and minus negative 33 R becomes plus 33 R minus negative seven becomes plus seven. OK? And all of that is still being divided by 13 R plus four. Now notice we have some common terms here because 19 R is like 33 R and nine is like seven. So we can combine those 19 R plus 33 R equals 52 R and nine plus seven equals 16. So 52 R plus 16 is all divided by 13 R plus four. Now, do you think we can go any further from here? Well, look at both of the terms or both expressions, don't you notice that the numerator is a multiple of the denominator? In other words, 52 R plus 16 is the same thing as four multiplied by 13 R plus four. Because 13 R into 52 R goes four times and four into 16 goes four times. So we can rewrite it as four multiplied by 13 R plus four, all divided by 13 R plus four. No notice, both of them have a common factor of 13 R plus four. So if we cancel those factors out, it leaves us with an answer of four. So that's our final answer. I can't get any simpler than that. Right. And when we look in our answer choices that would have been answer choice. Thanks a lot for watching everyone. I hope this video helped.

Add or subtract, as indicated. See Example 4. ((17y + 3)/(9y + 7)) - ((-10y - 18)/(9y + 7 ))

Key Concepts

Combining Like Terms

Adding and Subtracting Rational Expressions

Simplifying Algebraic Expressions

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