%2F(a-5).jpeg "(a^2-28)/(a-5)")
Simplifying the Expression (a^2 - 28)/(a - 5)
The expression (a^2 - 28)/(a - 5) represents a rational expression, which is a fraction where the numerator and denominator are polynomials. To simplify this expression, we can follow these steps:
1. Factor the numerator:
The numerator, a^2 - 28, is a difference of squares. We can factor it as: (a + √28)(a - √28)
2. Simplify the expression:
Now we can rewrite the original expression as: (a + √28)(a - √28) / (a - 5)
3. Identify any restrictions:
The expression is undefined when the denominator equals zero. Therefore, a ≠ 5.
Final Simplified Expression:
The simplified expression is: (a + √28)(a - √28) / (a - 5), where a ≠ 5
Note:
- We can further simplify the expression by substituting √28 = 2√7.
- This simplified form allows us to easily identify the values of 'a' for which the expression is defined and undefined.
- The simplified expression can be used for various mathematical operations, such as solving equations, finding the domain and range, or analyzing the behavior of the expression.