(3n%2B2%2F3n-2).jpeg "(2n/6n+4)(3n+2/3n-2)")
Simplifying Rational Expressions: (2n/6n+4)(3n+2/3n-2)
This article explores the process of simplifying the rational expression: (2n/6n+4)(3n+2/3n-2).
Step 1: Factoring
The first step in simplifying this expression is to factor out any common factors from the numerator and denominator of each fraction.
- Fraction 1 (2n/6n+4): We can factor out a 2 from both terms in the denominator:
- (2n / 2(3n+2))
- Fraction 2 (3n+2/3n-2): This fraction cannot be factored further.
Step 2: Cancellation
Now that we have factored the expressions, we can cancel out any common factors that appear in both the numerator and denominator. Notice that (3n+2) is a factor in both the numerator of fraction 1 and the denominator of fraction 2.
- (2n / 2(3n+2)) * (3n+2 / 3n-2)
After canceling out the (3n+2) factors, we are left with:
- (2n / 2) * (1 / 3n-2)
Step 3: Simplifying
Finally, we can simplify the remaining expression by canceling out the common factor of 2 in the first fraction:
- (n / 1) * (1 / 3n-2)
- n / (3n-2)
Conclusion
Therefore, the simplified form of the rational expression (2n/6n+4)(3n+2/3n-2) is n/(3n-2).
Important Note: This simplification is valid for all values of n except for n = 2/3, where the denominator becomes zero, resulting in an undefined expression.