3x over x^2 +10x +24 divided by x-6 over x^2 -36

Answer 1

To simplify this division problem, we need to first factor both the numerator and denominator.

First, let's factor the numerator: 3x over x^2 + 10x + 24

Factor the denominator: x - 6 over x^2 - 36

Numerator: 3x
Denominator: x - 6

The given expression can be rewritten as: (3x) / [(x+4)(x+6) / (x-6) / [(x+6)(x-6)]

Now, we need to simplify the expression by multiplying by the reciprocal:

3x / [(x+4)(x+6)] * [(x-6) / (x+6)(x-6)]

This simplifies to: 3x / (x+4)