Question

In the rational expression,


`(4x - 8)/(x ^(2) + 4x - 12)`
Why is it incorrect to cancel the 4x in the numerator with the 4x in the denominator? ​

Answer 1

The reason why it is incorrect to cancel the 4x in the numerator with the 4x in the denominator is because 4x is not a factor of both the numerator and the denominator

Explanation:

The denominator of the rational expression, x^2 + 4x - 12 given above is a quadratic equation. It is not factorizable. If we factorize the numerator, 4x - 8, we would have

4 (x - 2).

This means 4x is not a factor of the numerator(4x - 8) and neither is it a factor of the denominator (x^2 + 4x - 12). This is the reason why it is incorrect to cancel the 4x in the numerator with the 4x in the denominator. The factors of the denominator can only be gotten by using the general formula for solving quadratic equations