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## Algebra (all content)

### Course: Algebra (all content)>Unit 7

Lesson 14: Combining functions

# Dividing functions

Sal solves the following problem: given that f(x)=2x^2+15x-8 and g(x)=x^2+10x+16, find (f/g)(x). He explains that generally, (f/g)(x)=f(x)/g(x). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• At , Sal said that x couldn't be equal to negative 2 or negative 8, otherwise g(x) would be zero. However, in his answer, he only mentioned the condition that x not be equal to negative 8. Should he also have mentioned that x could not be equal to negative 2? •  Sal didn't mention negative 2 because (x+2) it is still present in the denominator, so we can tell that function is undefined just looking at it. However, since we divided numerator and denominator by (x+8) we can't say by the look of it that original function is undefined at -8. Hence we put only one condition, second one is seen from the simplified function.
• Where can I find Functions and Difference Quotients? • Why can't you just simplify by crossing things out? Also, how would I know whether to use factoring to simplify or not? I crossed out the x^2's and x's. Then, I simplified anything else to simpler, prime numbers to get 2+3-1/2+2 which is equal to 4/4 which is equal to 1. Therefore, I got (f/)(x)= 1. I feel like I am doing something wrong, but I don't know what. I also want to figure out how I can catch my mistake or prevent me from making this mistake if another problem like this comes up. • I'm confused. why is x squared plus ten x plus 16=(x+2)(x+8)? • I lost him at about ; What does he mean by defined? What is he talking about? • Sal says, " [ f(x) / g(x) ] is not defined when g(x) is equal to 0". When dividing anything by 0, we always end up with an UNDEFINED value. Mathematicians say this because, we still aren't really sure what it means to divide by 0, it is debated to this day. The answer to anything divided by 0 is unknown or not defined by anyone. Therefore if the function of g or g(x) turns out to be 0, than f(x) would be divided by 0, and we would not end up with an actual number output. Because we want a DEFINED answer, g(x) CANNOT equaal 0.
Hope this helps!
• Isn't there two restrictions for the new function -8 & -2? • What is the difference between the original function and the final function?
(1 vote) • @ sal said using the quadatic formula
What is it • From on, how does this 2x(x + 8) - 1(x + 8) work? • Factoring `2x(x + 8) - 1(x + 8)` into `(x+8) (2x-1)` uses the distributive property to factor out the common factor of (x+8). This is exactly the same process as factoring `2xy -1y` into `y(2x-1)`. The only difference is that in one case the common factor is a single variable "y" and the other case the common factor is a binomial "(x+8)" 