Write 2x/3x in simplest form
The Correct Answer and Explanation is:
The expression ( \frac{2x}{3x} ) can be simplified by canceling out the common factor in both the numerator and the denominator. Here’s a step-by-step explanation of the process:
Step 1: Identify Common Factors
The expression ( \frac{2x}{3x} ) consists of two terms: ( 2x ) in the numerator and ( 3x ) in the denominator. We notice that both the numerator and the denominator contain a factor of ( x ).
Step 2: Cancel Out Common Factors
We can simplify the expression by canceling the common factor of ( x ) from the numerator and the denominator, as long as ( x \neq 0 ) (since division by zero is undefined). This leaves us with:
[
\frac{2x}{3x} = \frac{2}{3}
]
Step 3: Verify Simplification
After canceling the common ( x ), the remaining terms are ( 2 ) in the numerator and ( 3 ) in the denominator. Since there are no more common factors between the numerator and the denominator, the fraction is in its simplest form.
Conclusion
Thus, the simplest form of ( \frac{2x}{3x} ) is ( \frac{2}{3} ), assuming that ( x \neq 0 ).
Additional Notes
This simplification process is based on the principle that when dividing two algebraic expressions, you can cancel out any common factors in the numerator and denominator. However, it’s essential to remember that you cannot cancel terms that are not factors. For example, you can’t cancel the ( x ) in ( 2x ) with the 3 in ( 3x ) because they are not common factors in the traditional sense.
In general, when simplifying rational expressions, always look for factors that can be divided out. If no common factors are present, the expression is already in its simplest form.