For these problems, treat each as its own problem, with different meanings for g(x) or f(x) than each other or examples we’ve used previously.

Question

g(t)=t+1

h(t)=3t−3

Find g(t)÷h(t)

f(x)=4x+4

g(x)=x^2+2

Find f(x)⋅g(x)

g(x)=−4x−2

h(x)=x^2−5x

Find h(x)⋅g(x)

Answer 1

Jeremiah, I'm not sure what's preventing you from answering these questions, and I would be happy to do them with you. Since you have three questions here, I'll show you how to do the first one.

You just need to sub the equations into the expressions. Since g(t)=t+1 and h(t)=3t−3, g(t)÷h(t) = (t+1)÷(3t-3).

Factor three from the denominator so it's 3(t-1). Since that looks a bit like the numerator, think about what you might be able to do to make them match...

If you multiply the denominator by -1, you get 3(1-t).

Multiplying the numerator by -1 also gives (1-t).

Doing these three things, We come out with (-1(1-t))÷(-3(1-t)), and the (1-t) cancels out. Then we have -1÷-3 = 1/3.

For the next two, just distribute your terms to multiply the two expressions. Here's the set up for the second question:

f(x)=4x+4

g(x)=x^2+2

f(x)⋅g(x) = (4x+4)(x²+2)

Distribute or use FOIL to multiply, and you're done!

I hope this helps, and happy mathing!

Liz Z.