Could someone help with this please?

Question

Multiply or divide as indicated. Be sure to reduce all answers to lowest terms.

 

2a²+14a+24/4a²-64 • 2a²-12a+16/a²+a-6

Answer 1

Funny running into you here....AGAIN!!! Boy, you don't sleep much, do you?!! Ok, Sunshine, let's start!!

 

No division here, so no flipping fractions.

And taking a closer look at each numerator and denominator, we see lots of reducing.

 

2a² + 14a + 24    what do you "see" that they have in common?

 

If you answered....each term can be reduced by 2....you would be CORRECT!! Give this gal an apple! Yeah, sorry...I'm a vegan! No candy treats in sight!

So, let's pull out that 2..... 2(a² + 7a + 12)

 

Take the next one.....4a² - 64     what do you "see?"

If you answered....each term can be reduced by 4....you would be CORRECT!! Give this gal an orange!!!!!

So, let's pull out that 4....   4(a² - 16).......oh but wait! There's another rule that applies here....the difference of perfect squares......OH MY!!!!!  The (a² - 16) can be factored into (a - 4)(a + 4)....which means now we have 4(a - 4)(a + 4)

 

Once we've factored all the numerators and denominators, we have.....

 

2(a + 3)(a + 4)          2(a - 2)(a - 4)

-------------------   •    ------------------

4(a - 4)(a + 4)             (a - 2)(a + 3)

 

Go ahead and reduce where possible and let me know what you get as an answer.