%C3%B76(x%2B5).jpeg "(4x^2-100)÷6(x+5)")
Simplifying the Expression (4x² - 100) ÷ 6(x+5)
This expression represents a division of two algebraic expressions:
- Dividend: (4x² - 100)
- Divisor: 6(x+5)
To simplify this expression, we can follow these steps:
1. Factor the Dividend
The dividend (4x² - 100) is a difference of squares. We can factor it as:
(4x² - 100) = (2x + 10)(2x - 10)
2. Simplify the Divisor
The divisor 6(x+5) can be left as it is.
3. Rewrite the Expression
Now we can rewrite the original expression as:
[(2x + 10)(2x - 10)] ÷ 6(x+5)
4. Cancel Common Factors
Notice that both the dividend and divisor have a common factor of (2x + 10):
- Dividend: (2x + 10)(2x - 10)
- Divisor: 6**(2x + 10)**
We can cancel this common factor:
(2x - 10) ÷ 6
5. Final Simplification
The final simplified form of the expression is:
(x - 5) ÷ 3
Therefore, the simplified form of (4x² - 100) ÷ 6(x+5) is (x - 5) ÷ 3.
Important Note: This simplification is valid only when x ≠ -5, because the original expression is undefined for x = -5 due to division by zero.