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

Question

Accepted Answer

Hey everyone here we are asked to divide and simplify the given expression where we have the quantity of three p minus 18 divided by 15. And this is divided by our second fraction here which is the quantity of seven p minus 42 divided by three. Now our first step here in dividing this expression is to recall that when we divide by a fraction we actually need to multiply by its reciprocal. So doing this, we rewrite our expression as the quantity of three P minus 18 divided by 15. And now we multiply by the reciprocal of our second fraction which will be three divided by the quantity of seven p.m. minus 42. So now our next step is to start simplifying. And so we first want to factor our expression as much as possible. So beginning with our first numerator we see that we have three p minus 18. Well both of these terms have a common factor of three. So factoring out the three, we have three times the quantity of p minus six. And again this is all divided by the same denominator of 15. And now we multiply by our second fraction where we will keep the numerator the same for now as just three and this is divided by this quantity of seven p minus 42. While both of these terms have a common factor of seven, So factoring out the seven, our denominator becomes seven times the quantity of P -6. And so now we see that since we have factored our expression as much as possible, we actually can perform some cancelations. So here we have P -6 in the first numerator and we also see that this appears in the second denominator. So both of these terms can. And so now we can rewrite our expression with what we have left. So we just have three times three divided by 15 times seven. So now we can see that a three in the numerator can cancel out with the 15 in the denominator but divided by three is just five. So we'll still be left with five. But now again rewriting our expression with what we have left, we have three divided by five times seven. So now just multiplying the terms in our denominator we are left with three divided by 35. And now there aren't any other simplifications that we can make. So this is our final simplified answer, which is answer choice C Thanks for watching. I hope you found this video helpful and I'll see you again next time

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

Key Concepts

Dividing Rational Expressions

Factoring Polynomials

Simplifying Rational Expressions

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