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ACT Math 2.1 Intermediate Algebra 359 Views


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Description:

ACT Math Intermediate Algebra Drill 2, Problem 1. Solve the equation.

Language:
English Language

Transcript

00:02

Try this shmoopy question on for size...

00:05

Solve: The quantity a squared minus a minus 12 all over the quantity a squared plus 3a

00:10

plus 2 divided by the quantity a plus 3 over the quantity a plus 2.

00:15

And here are the potential answers...

00:20

Well, there are really 2 major steps going on here.

00:23

One: multiplying by the inverse -- so we have to flip the 2nd fraction around and make

00:27

it times rather than divided by...

00:30

And then two: We clearly have a factorable expression here.

00:33

For the first one we have an a in each of these parts of the parentheses...

00:37

...then we have to figure out what 2 numbers multiply together to get negative 12 and also

00:41

add together to get negative 1.

00:44

What are the factors of 12? 1 and 12? Yeah... but that won't work.

00:49

2 and 6 don't work either, because when added, no matter which is positive and which

00:54

is negative, they won't total "1."

00:56

3 and 4 however... DO work.

00:59

So we want the ADDED part to be a negative 1... negative 4 plus 3 is negative 1, and

01:06

negative 4 times 3 is negative 12, so... we're good.

01:09

The first part of our answer is quantity a plus 3 times quantity a minus 4.

01:14

Now to the denominator.

01:16

We need 2 numbers that when multiplied are 2... and when added are 3.

01:20

Well... 2 only has 2 and 1 as factors... and luckily, if we add 2 and 1 we get 3. So the

01:26

bottom is a quick calculation.

01:26

It's quantity a plus 2 times quantity a plus 1.

01:29

Now we just rewrite everything so it's fully factored and... cross-out-able.

01:34

The quantity a plus 3 over the quantity a plus 3 becomes 1; we can trash it.

01:39

Same deal with the quantity a plus 2.

01:41

And we are left with just quantity a minus 4 over a plus 1...

01:45

...and the answer is C.

01:48

Phew.

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