QuestionSimplify the product
The answer is
Select one:
a.
b.
c.
d.
Studdy Solution
STEP 1
What is this asking?
We're asked to simplify a product of two fractions with in them, and then we need to make sure our simplified fraction isn't broken when is -6, 0, or 1.
Watch out!
We need to be super careful when simplifying, making sure we don't accidentally divide by zero!
Also, we gotta remember to check our simplified answer with those given values of .
STEP 2
1. Factor Everything
2. Simplify the Expression
3. Check for Restricted Values
STEP 3
Alright, let's **factor** the first fraction!
We've got .
Both the top and bottom have a , so we can factor that out on the bottom, giving us .
STEP 4
Now, let's look at the second fraction: .
We can factor out from the top, which gives us .
And we can factor out from the bottom, giving us .
So, the second fraction becomes .
STEP 5
Now, let's put it all together and see what cancels out!
We have .
STEP 6
We can divide to one a from the top and bottom of the first fraction, leaving us with .
We can also divide to one a from the top and bottom of the second fraction, giving us .
STEP 7
Now our expression is .
Let's multiply across!
That gives us .
STEP 8
We can factor a 2 from to get , which is the same as .
Now we have .
STEP 9
We can divide to one from the top and bottom, and we're left with .
We can also simplify by dividing both by 3, which gives us .
So, our final simplified expression is .
STEP 10
Let's check if our simplified expression works with , , and .
STEP 11
If , we get .
No problem there!
STEP 12
If , we get .
Looks good!
STEP 13
If , we get .
Uh oh!
We can't divide by zero, so is a **restricted value**.
STEP 14
The simplified expression is , which is answer choice (a).
We also found that cannot be equal to **1**.
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