Multiply or divide, as indicated. See Example 3. ((4a + 12) / ...

Question

Multiply or divide, as indicated. See Example 3. ((4a + 12) / (2a - 10)) ÷ ((a² - 9) / (a² - a - 20))

Accepted Answer

Hey, everyone, here we are asked to perform the indicated operations and simplify the given rational expression. Nine Y plus 27 all divided by three, Y minus 15, divided by Y squared minus nine all divided by Y squared minus three, Y minus 10. Here we have four answer choice options. Answer choice A three multiplied by the quantity of Y minus two divided by Y minus three. Answer B three multiplied by the quantity of Y plus two divided by Y minus three. Answer cy plus two, all divided by three, multiplied by the quantity of Y plus three and answer dy minus two all divided by three multiplied by the quantity of Y minus three. So to begin dividing our two given fractions, we first want to factor all of the numerators and denominators. So starting with our first fraction in the numerator again, we have nine Y plus 27. So here we can factor out nine from both terms. This gives us nine multiplied by the quantity of Y plus three. And now in the denominator, we have three, Y minus 15. And here we can factor out three. So we have three multiplied by the quantity of Y minus five. And now this is divided by our second fraction. Where in the numerator, we have two perfect squares of which we can factor into the quantity of Y plus three multiplied by the quantity of Y minus three. And in the denominator, we have a trinomial which factors into the quantity of Y minus five multiplied by the quantity of Y plus two. And now our next step in dividing our two fractions is recalling that when we divide by a fraction, it is the equivalent as multiplying by its reciprocal. So we just want to rewrite our division as multiplication. So we have nine multiplied by the quantity of Y plus three divided by three multiplied by the quantity of Y minus five. And now we multiply by the reciprocal of our second fraction. So we multiply by the quantity of Y minus five multiplied by the quantity of Y plus two, all divided by the quantity of Y plus three multiplied by the quantity of Y minus three. And now that we are multiplying both of our fractions together, we can begin reducing common common expressions in both of the fractions. So in our first fraction, we have Y plus three in the numerator which cancels with the Y plus three in the denominator of the second fraction. And then in the second fractions numerator, we have Y minus five which cancels with the Y minus five in the first fractions denominator and now continuing to reduce, we also have nine divided by three, which simplifies to just three. So now writing our new expression with all of our simplifications, we have three multiplied by the quantity of Y plus two, all divided by Y minus three. And with this, we see there are no more simplifications that we can make. So this is our final expression which leaves us with answer choice B where again, our final expression is three multiplied by the quantity of Y plus two divided by Y minus three. 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. ((4a + 12) / (2a - 10)) ÷ ((a² - 9) / (a² - a - 20))

Key Concepts

Polynomial Factorization

Division of Rational Expressions

Simplification of Algebraic Fractions

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