Multiply or divide, as indicated. See Example 3. ((2k + 8) / 6...

Question

Multiply or divide, as indicated. See Example 3. ((2k + 8) / 6) ÷ ((3k + 12) / 2)

Accepted Answer

Hey, everyone here we are asked to perform the indicated operations and simplify for the given rational expression. Seven H plus 21 all divided by four divided by two H plus six, all divided by two. Here we have four answer choice options, answer choice A eight divided by seven, answer B seven divided by eight, answer C four divided by seven and answer D seven divided by four. So before we begin dividing our two given fractions, we first want to factor the fractions as much as possible. So starting in the numerator of our first fraction again, recalling we have seven H plus 21. Here we see both terms share the value of seven. So factoring out seven, we have seven multiplied by the quantity of H plus three. And this is all still divided by four. Since four cannot be simplified, then we are dividing by our second fraction which again in the enumerator has two H plus six. Here, both terms share the value of two. So factoring out two, we have two multiplied by the quantity of H plus three and this is all divided by two. And now we see in our second fraction that we can make an immediate simplification since we have two in the numerator as well as two in the denominator. So both of the twos cancel out and become one. And so writing our simplified expression so far, we have seven multiplied by the quantity of H plus three, all divided by four, divided by the quantity of H plus three divided by one. And now we want to rewrite our current expression by recalling the fact that when we divide by a fraction, it is the same as multiplying by its reciprocal. So rewriting, we have seven multiplied by the quantity of H plus three, all divided by four, multiplied by one divided by the quantity of H plus three. And now that we are multiplying our two fractions together, we can begin simplifying further by noticing that we have H plus three in the numerator of the first fraction. And we have this same expression H plus three in the denominator of our second fraction. So both of these expressions cancel out. And so now just rewriting our simplified expression, we are left with just seven divided by four. And now we see there are no further simplifications that we can make. So this is our final answer here which leaves us with answer choice D where again, we have seven divided by four. 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. ((2k + 8) / 6) ÷ ((3k + 12) / 2)

Key Concepts

Multiplication and Division of Fractions

Factoring Algebraic Expressions

Simplifying Rational Expressions

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