-2%2Fa%2B6.jpeg "(1/a-6 - 1/a+6) 2/a+6")
Simplifying the Expression: (1/a-6 - 1/a+6) * 2/(a+6)
This expression involves fractions and requires us to simplify it using the rules of algebra. Here's a step-by-step breakdown:
Step 1: Finding a Common Denominator for the Fractions
The first part of the expression (1/a-6 - 1/a+6) has two fractions with different denominators. To subtract them, we need a common denominator. The least common denominator for (a-6) and (a+6) is simply their product: (a-6)(a+6).
Let's rewrite each fraction with this common denominator:
- 1/a-6 = (a+6)/(a-6)(a+6)
- 1/a+6 = (a-6)/(a-6)(a+6)
Now we can subtract the fractions:
(a+6)/(a-6)(a+6) - (a-6)/(a-6)(a+6) = (a+6 - (a-6))/(a-6)(a+6) = 12/(a-6)(a+6)
Step 2: Multiplying by the Remaining Fraction
Now our expression looks like this: 12/(a-6)(a+6) * 2/(a+6)
To multiply fractions, we multiply the numerators and the denominators:
(12 * 2)/((a-6)(a+6)(a+6)) = 24/((a-6)(a+6)^2)
Conclusion
The simplified form of the expression (1/a-6 - 1/a+6) * 2/(a+6) is 24/((a-6)(a+6)^2). Remember, this result is valid for any value of 'a' except for a = 6 and a = -6, as those values would make the denominator zero, leading to an undefined expression.