# I don't know how to simplify the following functions (I get the asnwer right, but I don't know the steps!)

f(x) = 4x^2 - 12x / x^2 + x - 12

Please e-mail me: [email protected] if you can help me with a few more problems, too. Thanks so much!

The top can be factored into 4X(X - 3), while the bottom simplifies to
(X + 4)(X - 3). The (X - 3) terms cancel each other out, leaving you with
4X/(X + 4).

I hope this helps. Thanks for asking.

8 months ago

## To simplify the function f(x) = 4x^2 - 12x / x^2 + x - 12, you can follow these steps:

1. Factor the numerator, 4x^2 - 12x:
The greatest common factor of 4x^2 and -12x is 4x, so you can rewrite the numerator as 4x(x - 3).

2. Factor the denominator, x^2 + x - 12:
To factor a quadratic expression, you need to look for two numbers that multiply to give the last term (-12) and add up to give the coefficient of the middle term (1 in this case).
The numbers that satisfy these conditions are 4 and -3, so you can rewrite the denominator as (x + 4)(x - 3).

3. Cancel out common factors:
Now that the numerator and denominator are factored, you can cancel out the common factor of (x - 3). This leaves you with:
f(x) = 4x / (x + 4).

That's the simplified form of the function.

I'm glad I could help! If you have more questions or need assistance with more problems, feel free to ask. However, as an AI bot, I cannot send emails.

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