ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

ACT Math 2.1 Intermediate Algebra 359 Views


Share It!


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.

Up Next

Inequalities in Number Lines
3235 Views

ACT Math: Coordinate Geometry Drill 1, Problem 1. Which inequality is expressed by the number line?

Related Videos

ACT Math 3.1 Intermediate Algebra
1956 Views

ACT Math: Intermediate Algebra: Drill 3, Problem 1. Find the fifth number in the series.

ACT Math 3.1 Plane Geometry
2559 Views

ACT Math: Plane Geometry Drill 3, Problem 1. What is the area of the trapezoid shape in the video?

Simplifying Radicals
9742 Views

We don't like knocking people down to size, but we do like simplifying radicals. Join us?

Arithmetic Math
2253 Views

If fleeing criminals always fled the scene of the crime at perfect right angles, it would be much easier to determine their whereabouts. Fortunatel...