Simplify x^2 - 3x - 18/x+3

Answers
x-3
x-6 where x doesn't equal -3
x-6 where x doesn't equal 6
1/x+3 where x doesn't equal -3

I am going off line for the afternoon.

Hope somebody else picks up your questions.

for this one,

Hint:

= (x-6)(x+3)/(x+3)
= ...

To simplify the expression (x^2 - 3x - 18)/(x + 3), we can factor the numerator and denominator separately and then cancel out any common factors.

Step 1: Factor the numerator (x^2 - 3x - 18)

We can factor the quadratic expression x^2 - 3x - 18. To do this, we need to find two numbers whose product is -18 and whose sum is -3. The numbers that satisfy these conditions are -6 and +3. So, we can rewrite the numerator as follows:

x^2 - 3x - 18 = (x - 6)(x + 3)

Step 2: Factor the denominator (x + 3)

The denominator is already in its simplest form as x + 3 and cannot be factored further.

Step 3: Cancel out common factors

Cancel out the common factor of (x + 3) in the numerator and denominator:

(x - 6)(x + 3)/(x + 3)

The (x + 3) term in the numerator can be cancelled out with the (x + 3) term in the denominator:

(x - 6)

Therefore, the simplified expression is x - 6. However, there is a restriction on the value of x. We cannot have x = -3 because it would result in division by zero, which is undefined.

So, the final simplified expression is x - 6, where x does not equal -3.