Question

How do you simplify and restricted value of `(x^2-36)/(3x+6)`?

Answer 1

`((x-6)(x+6))/(3(x+2))`; `x != -2`

Explanation:

Given: `(x^2 - 36)/(3x+6)`

The numerator is the difference of squares `(a^2 - b^2) = (a - b)(a + b): (x^2 - 6^2) = (x -6)(x+6)`

Rewriting the given expression yields: `((x -6)(x+6))/(3x + 6)`

The denominator can be factored using the greatest common factor (GCF) of `3: 3(x + 2)`

Rewriting the given expression yields: `((x-6)(x+6))/(3(x+2))`

Since there is a fraction, the denominator cannot be `= 0`. This means that `3(x + 2) != 0`, or `x + 2 != 0`. This occurs when `x = -2`.