I need some help with some algebra problems please.

I don't under stand how to do that following.

Find and simplify the difference quotient f(x+h) -f(x)/h, h cannot equal 0 for the given function.

1. f(x)=5x^2

2. f(x)x^2+3x+9

The first:

f(x+h)=5(x+h)^2=5x^2+10xh+5h^2

f(x+h)-f(x)= 5x^2+10hx + 5h^2-5x^2=
10hx +5h^2

divided by h

10x + 5h

as the limit of h>>0
10x

1. f(x) = 5x^2

To find the difference quotient for this function, we need to substitute f(x + h) and f(x) into the formula and simplify it.

The formula for the difference quotient is:
f(x + h) - f(x) / h

For our given function f(x) = 5x^2, let's substitute f(x + h) and f(x) into the formula:
f(x + h) = 5(x + h)^2
f(x) = 5x^2

Substituting these into the difference quotient formula, we get:
[5(x + h)^2 - 5x^2] / h

Now, let's simplify this expression:
[5(x^2 + 2xh + h^2) - 5x^2] / h

Expanding and simplifying further:
[5x^2 + 10xh + 5h^2 - 5x^2] / h

Canceling out the common terms, we have:
[10xh + 5h^2] / h

Factoring out an h from the numerator, we get:
h(10x + 5h) / h

Canceling out the h terms, we obtain:
10x + 5h

So, the simplified difference quotient for the function f(x) = 5x^2 is 10x + 5h.

Now, let's move on to the second problem.

2. f(x) = x^2 + 3x + 9

Using the same process as before, let's substitute f(x + h) and f(x) into the difference quotient formula:

f(x + h) = (x + h)^2 + 3(x + h) + 9
f(x) = x^2 + 3x + 9

Substituting these into the formula, we get:
[(x + h)^2 + 3(x + h) + 9 - (x^2 + 3x + 9)] / h

Simplifying further:
[x^2 + 2xh + h^2 + 3x + 3h + 9 - x^2 - 3x - 9] / h

Canceling out the common terms, we have:
[2xh + h^2 + 3h] / h

Factoring out an h from the numerator, we get:
h(2x + h + 3) / h

Canceling out the h terms:
2x + h + 3

So, the simplified difference quotient for the function f(x) = x^2 + 3x + 9 is 2x + h + 3.

I hope this helps you understand how to find and simplify the difference quotient for these two given functions. Let me know if you have any further questions!