How do you simplify #(4x-24)/(x^2-12x+36)# and what are the ecluded values fot he variables?

Question

Nathan Axel · Accepted Answer

Excluded value x=6

simplification is #4/(x-6)# The given expression in factorised form is #(4(x-6))/(x-6)^2#. If x=6, the given expression acquires an indeterminate form of type #0/0#. Thus x=6 is excluded from the the values which x can acquire. If x is excluded, the given expression simplifies to #4/(x-6)#

Eva Abramson · Answer

undefined To simplify (4x-24)/(x^2-12x+36), we can first factor the numerator and denominator. The numerator can be factored as 4(x-6), and the denominator can be factored as (x-6)(x-6).

Next, we can cancel out the common factor of (x-6) in both the numerator and denominator.

This leaves us with the simplified expression of 4/(x-6).

The excluded value for the variable x is 6, as it would result in a denominator of zero, which is undefined.

Savannah Anderson · Answer

undefined To simplify $ \frac{4x - 24}{x^2 - 12x + 36} $, follow these steps:

1. Factor both the numerator and denominator, if possible.

2. In this case, the numerator is already in its simplest form, but the denominator can be factored into $(x - 6)^2$.

3. Rewrite the expression with the factored form of the denominator:
$$ \frac{4x - 24}{(x - 6)^2} $$

4. Factor out any common factors from the numerator, if possible. In this case, 4 can be factored out:
$$ \frac{4(x - 6)}{(x - 6)^2} $$

5. Simplify further if possible. In this case, the $ (x - 6) $ in the numerator and denominator can be canceled out, leaving:
$$ \frac{4}{x - 6} $$

The excluded values for the variables are the values that would make the denominator equal to zero, as division by zero is undefined. In this case, the excluded value is $ x = 6 $, because if $ x $ were equal to 6, the denominator $ (x - 6) $ would be equal to zero. Therefore, $ x = 6 $ is excluded from the domain of the original expression.