2x^2+7x+3/x^2-2x-15

Do you mean..

(2x^2 +7x+3)/(x^2 -2x -15)

You have to factor the numerator and the denominator and remove the common factors.

Can you factor these or do you need help?

need help

[(2x+1)(x+3)]/[(x-5)(x+3)} = ?

Do you understand how you actually factor?

There is the guess method where you

would begin with:

x^2 -2x-15

(x- ) (x + )

I know that I need x in the front because x times x = x^2

I know that I need a plus and minus sign because 15 is negative and I will need to mulitply a + and a - number to get -15

Next, I have to think of two numbers that multiply to equal 15 and add to be -2 for the -2x portion.

It gets more complicated with 2x^2.. but it works basically the same way by guessing.

To simplify the expression (2x^2 + 7x + 3) / (x^2 - 2x - 15), we can first factor the numerator and the denominator and then cancel out any common factors.

Step 1: Factor the numerator (2x^2 + 7x + 3).
The expression is quadratic, so we need to find two binomials whose product is equal to 2x^2 + 7x + 3. The factors will have the form (ax + b)(cx + d).

To find a and c, we need to multiply them to get the coefficient of x^2. In this case, since the coefficient of x^2 is 2, a and c can be either 1 and 2 or 2 and 1.
The coefficient of x is 7, so one of the factors has a product of 7x. Since the sign is positive, we need to choose the factors that add up to 7x. The factors that satisfy these conditions are (2x + 1)(x + 3).

Step 2: Factor the denominator (x^2 - 2x - 15).
We need to find two binomials whose product is equal to x^2 - 2x - 15. The factors will have the form (ax + b)(cx + d).

To find a and c, we need to multiply them to get the coefficient of x^2. In this case, since the coefficient of x^2 is 1, a and c can be either 1 and 1.
The coefficient of x is -2, so one of the factors has a product of -2x. Since the sign is negative, we need to choose the factors that subtract to -2x. The factors that satisfy these conditions are (x - 5)(x + 3).

Step 3: Cancel out any common factors.
Now that we have factored both the numerator and the denominator, we can cancel out any common factors. In this case, (x + 3) appears in both the numerator and the denominator. So we can cancel it out.

The simplified expression is: (2x + 1) / (x - 5)