Add or subtract as indicated. 12/25x^2+11/15x^3

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Hello. Today we're going to be combining two fractions that have exponential values in their denominators. So the two fractions given to us is 5/2 X. To the fifth power plus 7/ X to the seventh power. Now in order to combine both of these fractions we need to go ahead and have the same values on both the dominators. So we need to go ahead and find a lowest common denominator between these two fractions. Well if we pay attention to two and three a similar factor that's between two and three is six. And if we look over here we have X to the fifth and X to the seventh. Whenever you are dealing with nominators that have exponential values you want to go ahead and keep the variable that has the highest power. So we're gonna want our L. C. B. D. To be six X. To the seventh power. So how do we change both of these fractions to have six X. To the seventh in their denominators? Well on the right hand side We already have X to the seventh in the denominator. So all we want to do is just go ahead and change this three in order to change 3-6 we just need to multiply this fraction by two in the denominator. And since we're multiplying by two in the denominator we're gonna multiply two to the numerator as well. Now what about the left hand side with 5/2 X to the fifth. Well the same thing occurs. We want to change 2 to 6. So in order to change 2 to 6 we're gonna multiply by three. But now the question is what do we multiply X to the fifth by to give us X to the seventh. Well let's recall our exponential multiplication. We have X to the fifth. And we're going to multiply that by another X. Exponential value of N. In order to give us X to the seventh. When multiplying two exponential factors with the same base. You're just going to add the exponents together. So that gives us X to the power of five plus N. Equal to X. To the seventh. And now we just want to go ahead and solve for a value of N. So we get five plus N equal to seven. In order to sulfur end. We're just gonna go ahead and subtract five to both sides. And that gives us N. Is equal to two. So that tells me that I want to go ahead and multiply X to the fifth by X squared. That way we can get X to the seventh in this denominator. And if we multiply this denominator by three X squared. We need to multiply the numerator by three X squared as well. So now let's just go ahead and multiply everything together. Three X squared times five is going to give me 15 X squared. And three X squared times two X to the fifth is going to give me six X to the seventh. And on the right hand side seven times two is gonna give me 14 and three X to the seventh. Power times two is gonna give me six X to the seventh. Now that I have the same denominator on both of these fractions, I'm gonna go ahead and combine both of them together. Doing so is gonna give me 15 X squared plus 14/6 X to the seventh. Power. This cannot be simplified any further. So this is going to be our solution that also tells us that the solution to this problem is going to be a So I hope this helps you understand how to combine exponential denominators together and I'll go ahead and see you all in the next video.

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