Question

X²+3x²-4x-12/(x-2)(x+3)

Answer 1

x^2+3x^2-4x-12/(x-2)(x+3)

x^2+3x^2-4x-12/(x^2+3x-2x-6)

x^2+3x^2-4x-12/x^2+x-6

3x^2-3x-2=0

D=b^2-4ac=9-4*3*(-2)=9+24=33

x1=(3+33)/6=36/6=6

x2=(3-33)/6=-30/6=-5

Answer 2

To simplify the expression, let's start by factoring the numerator:

x² + 3x² - 4x - 12

Step 1: Combine like terms: 4x² - 4x - 12

Step 2: Factor out the greatest common factor (GCF), which is 4: 4(x² - x - 3)

Now, we want to factor the quadratic expression inside the parentheses: x² - x - 3

To do that, we look for two numbers whose product is -3 and whose sum is -1 (since the coefficient of the x term is -1). Those numbers are -3 and 1: x² - x - 3 = (x - 3)(x + 1)

Now, the original expression becomes: (4)(x - 3)(x + 1)

Finally, let's divide this expression by the denominator (x - 2)(x + 3):

(4x - 12)/(x - 2)(x + 3)

Now, we can simplify it further if possible, but it looks like there's no common factor that can be simplified. So, the simplified expression is:

(4x - 12)/(x - 2)(x + 3)

If you need to simplify it further or evaluate it for a specific value of x, please provide more information or let me know what you'd like to do with this expression.