Add or subtract, as indicated. 1/a + b/a^2

Question

Accepted Answer

Hey everyone here we are asked to add and simplify the given expression where we have a church divided by k cubed plus three divided by K. Now our first step here in adding these two terms together is to recall that when we add fractions we need to find a common denominator. Well here we can see that our least common multiple is going to be K. Cute in and this is already the denominator of our first fraction. So we don't need to make any other changes to it. But looking at our second fraction, we see that in the denominator we have K to the first power. So in order to find what we need to multiply this second fraction by to get the common denominator, we need to recall the product rule for exponents which tells us that A to the p power of M times A. To the power of N is equal to A. To the power of M plus N. So with this formula we know that K to the first power times K. To the second power is equivalent to K. To the power of one plus two, which simplifies to just K to the power of three. So now we see we know that we need to multiply our second fraction by K squared. But we need to multiply both the numerator and the denominator by K squared. So we don't make any changes to the problem itself. So again multiplying the numerator and the denominator by case squared. So now we can rewrite our simplified expression here. So we have h divided by k cubed plus three times K squared divided by k cubed. And so now since we have a common denominator we can simply add the numerator is together. So doing this we have the quantity of H plus three times k squared divided by k cubed. And here we can see there aren't any other simplifications of which we can make. So this is our final simplified answer, which leaves us with answer choice B. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Add or subtract, as indicated. 1/a + b/a^2

Key Concepts

Rational Expressions

Common Denominator

Combining Fractions

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