Express in simplest form: 36x-216/x^2-36
To express the given expression in simplest form, we can first factor the numerator and denominator.
The numerator 36x - 216 can be factored as 36(x - 6).
The denominator x^2 - 36 is a difference of squares and can be factored as (x - 6)(x + 6).
Now we can cancel out the common factor (x - 6) in the numerator and denominator.
The simplified form of the expression is:
36(x - 6) / (x - 6)(x + 6)
The (x - 6) terms cancel out, resulting in:
36 / (x + 6)
To express the expression (36x - 216) / (x^2 - 36) in simplest form, we need to factor the numerator and the denominator.
The numerator, 36x - 216, can be factored by taking out the greatest common factor (GCF) of 36, which is 36. Therefore, we can rewrite the numerator as 36(x - 6).
The denominator, x^2 - 36, is a difference of squares and can be factored as (x - 6)(x + 6).
Now we can simplify the fraction by canceling out the common factor (x - 6) in the numerator and denominator:
(36(x - 6)) / ((x - 6)(x + 6))
The factor (x - 6) in the numerator and denominator cancels out:
36 / (x + 6)
Therefore, the simplest form of the expression (36x - 216) / (x^2 - 36) is 36 / (x + 6).
To express the given expression in simplest form, we need to simplify it by factoring and canceling out common terms.
The given expression is: (36x - 216) / (x^2 - 36)
Step 1: Factor the numerator and denominator.
The numerator can be factored as 36(x - 6), using the common factor of 36.
The denominator can be factored using the difference of squares formula: x^2 - 36 = (x - 6)(x + 6).
Now, the expression becomes: (36(x - 6)) / ((x - 6)(x + 6))
Step 2: Cancel out the common factor of (x - 6) in the numerator and denominator.
(x - 6) / (x - 6) = 1
(36(x - 6)) / ((x - 6)(x + 6)) simplifies to 36 / (x + 6)
Therefore, the simplest form of the given expression is 36 / (x + 6).