Hi I am learning about rational expression and so far I am pretty good at multiplying. My question is how do you divide?
Here is a problem that I am having trouble with..
6p-18 3p-9
----- / ----
9p p²+2p
This is what I have so far
6(p-3) 3(p-3)
------ / ------
9p p(p+2)
Can you show me what is next? Thanks.
You are OK so far.
[6(p-3)/(9p)]/{3(p-3)/[p(p+2)]} =
6(p-3) p(p+2)
------ x ------ =
9p 3(p-3)
[6/9] x [(p+2)/3] =
(2/9)(p+2)
To divide rational expressions, you can follow these steps:
1. Keep the first fraction as it is.
2. Change the division sign to multiplication.
3. Invert the second fraction by swapping the numerator and denominator.
4. Simplify, if possible, by canceling out common factors.
Let's apply these steps to your problem:
The given expression is:
(6p-18)/(9p) divided by (3p-9)/(p^2+2p)
Step 1: Keep the first fraction as it is:
(6p-18)/(9p)
Step 2: Change the division sign to multiplication:
(6p-18)/(9p) * (p^2+2p)/(3p-9)
Step 3: Invert the second fraction:
(6p-18)/(9p) * (p^2+2p)/(3p-9) = (6p-18)/(9p) * (p^2+2p)/(3p-9)
Step 4: Simplify, if possible, by canceling out common factors:
In the numerator, we can factor out 6 from (6p-18) to get:
6(p-3)
In the denominator, we can factor out 9p from (9p) to get:
9p
For the second fraction, we can factor out 3 from (3p-9) to get:
3(p-3)
And in (p^2+2p), there are no common factors.
So, after simplifying the expression, we have:
[6(p-3)/(9p)] * [(p^2+2p)/(3(p-3))]
Now, if there are any common factors left, you can cancel them out. In this case, the (p-3) factor in the numerator and denominator can be canceled out:
6p/(9p) * (p^2+2p)/3
Now, you can simplify each fraction separately:
6p divided by 9p simplifies to 2/3.
And (p^2+2p) divided by 3 remains the same.
Therefore, the final simplified expression is:
(2/3)(p^2+2p)