Simplify by first factorising the numerator and denominator:
(x^2-x-12)/(〖5x〗^2+20x) ÷ (x+3)/15
To simplify the expression, let's first factorize the numerator and denominator separately.
Factorizing the numerator (x^2 - x - 12):
The numerator can be factored as (x - 4)(x + 3).
Factorizing the denominator (5x^2 + 20x):
The denominator can be factored as 5x(x + 4).
Now, let's rewrite the expression with the factored forms:
[(x - 4)(x + 3)] / [5x(x + 4)] ÷ (x + 3) / 15
Next, we can simplify the expression by canceling out common factors in the numerator and denominator:
[(x - 4)(x + 3)] / [5x(x + 4)] * [15 / (x + 3)]
After canceling out the common factor (x + 3) in the numerator and denominator, we get:
[(x - 4) * 15] / [5x * 1]
Therefore, the simplified expression is:
(15x - 60) / (5x)
or
3(x - 4) / x