Simplify.
x^2+3x+2/x^2-2x-3
To simplify the expression (x^2 + 3x + 2) / (x^2 - 2x - 3), we can factor both the numerator and denominator and then cancel out any common factors.
Let's start by factoring the numerator:
x^2 + 3x + 2
We look for two numbers whose sum is 3 and whose product is 2. The numbers that satisfy these conditions are 1 and 2. Therefore, we can rewrite the numerator as:
(x + 1)(x + 2)
Next, let's factor the denominator:
x^2 - 2x - 3
We look for two numbers whose sum is -2 and whose product is -3. The numbers that satisfy these conditions are -3 and 1. Therefore, we can rewrite the denominator as:
(x - 3)(x + 1)
Now, we rewrite the expression with the factored forms:
(x + 1)(x + 2) / (x - 3)(x + 1)
Notice that (x + 1) appears in both the numerator and denominator. We can cancel out the common factor, leaving us with:
(x + 2) / (x - 3)
And there you have it! The simplified form of the expression (x^2 + 3x + 2) / (x^2 - 2x - 3) is (x + 2) / (x - 3).