(2n/6n+4)(3n+2/3n-2)

2 min read Jun 16, 2024
(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.

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