Sarah is simplifying the rational expression
3x + 6
-----------
3x
She cancels the 3x's and states that the answer is 6. Matt tells her that she is incorrect. What is one example that he could use to show her that this is incorrect?
4 + 6
------- ≠ 6
4
B) 6
------ ≠ 4
4 + 6
C) 4 + 6
-------- ≠ 2
4 + 3
D) 4
------- ≠ 1/6
4 + 6
I think its B
nvm its 8
To show Sarah that cancelling the 3x's and stating that the answer is 6 is incorrect, Matt could use the following example:
D) 4
------- ≠ 1/6
4 + 6
Let's break down how Matt reached this example:
First of all, he noticed that Sarah cancelled the 3x's in both the numerator and the denominator of the rational expression. Canceling out terms in this manner is only valid if the terms are the same and can be completely reduced.
In the given expression, the 3x in the numerator and the 3x in the denominator are indeed the same. However, the remaining terms are not the same, which is a crucial factor.
To explain why Sarah's approach is incorrect, Matt used the example D:
In the example, the numerator is 4, and the denominator is 4 + 6. Sarah would have cancelled the 4's and concluded that the resulting expression is equal to 1/6. However, this is not true.
To determine if two rational expressions are equal, we need to simplify them and see if they result in the same value for all valid values of x. Instead of canceling the terms, Matt simplifies the example expression:
4
-- ≠ 1/6
4 + 6
By adding 4 + 6, the denominator becomes 10. Now we have:
4
-- ≠ 1/6
10
The fraction 4/10 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
4/10 simplifies to 2/5.
Therefore, Matt's example shows that the original expression, when simplified correctly, doesn't equal to the answer Sarah stated.