Multiply or divide, as indicated. See Example 3. ((x² + x) / 5...

Question

Multiply or divide, as indicated. See Example 3. ((x² + x) / 5) • 25 / (xy + y)

Accepted Answer

Hey, everyone here we are asked to perform the indicated operations and simplify the given rational expression U squared plus two U all divided by seven, multiplied by one divided by Vu plus two V. Here we have four answer choice options, answer choice, A seven divided by Vu answer BVU divided by seven answer CV, divided by seven U and answer du divided by seven V. So before we begin multiplying our two given fractions together, we first want to start factoring the numerators and denominators as much as possible. So starting in the numerator of our first fraction, we again have U squared plus two U. Well, here we see both terms in the numerator share the variable U. So we can factor it out. So we have U multiplied by the quantity of U plus two. And in the denominator, there is no factoring that we can do. So this is all just divided by seven. And similarly with the numerator of the second fraction, we just have one which cannot be factored. And then in the denominator, we have Vu plus two V where we see both terms share V. So we can factor it out which gives us V multiplied by U the quantity of U plus two. So now we can start simplifying since we are multiplying both fractions together. And here we see that we have U plus two in the numerator of our first fraction. And we also have the same expression U plus two in the denominator of our second fraction. So both of these expressions cancel out since we have one in the numerator and one in the denominator. So now we can just start simplifying. So we have U divided by seven, multiplied by one divided by V. And now we have simplified both fractions as much as possible. So we can just begin multiplying the numerators and the denominators together. So U times one gives us U divided by seven times V which is just seven B. So now we have found our fully simplified expression which leaves us with answer choice D where again, we have U divided by seven V. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Multiply or divide, as indicated. See Example 3. ((x² + x) / 5) • 25 / (xy + y)

Key Concepts

Algebraic Expression Simplification

Multiplication and Division of Rational Expressions

Factoring Polynomials

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