simplifying 3x^2+3x-36/x^2-x-6 and what are the restrictions and also the steps
I am sure you meant
(3x^2+3x-36)/(x^2-x-6)
= 3(x+4)(x-3)/((x-3)(x+2)
= 3(x+4)/(x+2) , x ≠ 3
post it.
To simplify the expression 3x^2 + 3x - 36 / (x^2 - x - 6), we need to factorize the numerator and denominator, then cancel out any common factors.
Step 1: Factorize the numerator (3x^2 + 3x - 36).
To factorize, first check if there is a common factor among the coefficients (in this case, 3). If so, factor it out. Then, find two numbers that multiply to give the constant term (-36) and add up to give the coefficient of x (3).
3x^2 + 3x - 36
= 3(x^2 + x - 12)
Next, we need to factorize the quadratic expression in the parentheses. We look for two numbers that multiply to give the constant term (-12) and add up to give the coefficient of x (1).
x^2 + x - 12
= (x - 3)(x + 4)
So, the numerator becomes:
3(x - 3)(x + 4)
Step 2: Factorize the denominator (x^2 - x - 6).
We need to find two numbers that multiply to give the constant term (-6) and add up to give the coefficient of x (-1).
x^2 - x - 6
= (x - 3)(x + 2)
So, the denominator becomes:
(x - 3)(x + 2)
Step 3: Cancel out common factors between the numerator and the denominator.
Now that we have factored both the numerator and the denominator, we can cancel out the common factors:
(3(x - 3)(x + 4)) / ((x - 3)(x + 2))
The (x - 3) terms cancel out, leaving us with:
3(x + 4) / (x + 2)
This is the simplified form of the expression.
Restrictions:
To find the restrictions, we need to find the values of x for which the denominator becomes zero since division by zero is undefined.
Setting the denominator equal to zero, we get:
(x - 3)(x + 2) = 0
Solving for x, we find that x can take two values:
x - 3 = 0 --> x = 3
x + 2 = 0 --> x = -2
So, the restrictions are x ≠ 3 and x ≠ -2.