# Slope of a tangent line

Find the slope of the functions graph at the given point.

F(x) = x / x-2 point (3,3)

f(x+h) - f(x) / h is what we have to use to find the answer.

so ive plugged it all in and have came to this..

((3+h) / (3+h-2)) - 3 / h

I need some help with my simplification skills. I do not know how to get rid of a fraction in a fraction in this case im guessing. Where would I need to go next?

CompuChip
Homework Helper
By lack of brackets (and by the question) I assume you mean
$$\frac{\frac{3+h}{3 + h - 2} - 3}{h}$$

You can start by simplifying 3 + h - 2.
Next, look at the numerator
$$\frac{3 + h}{3 + h - 2} - 3$$
and write it as a single fraction:
$$\frac{...}{3 + h - 2}$$

Then you have something of the form
$$\frac{a}{b} / c$$
multiply by 1 in the form: b/b which will give you
$$\frac{ab}{b} / (bc) = a / (bc)$$

By lack of brackets (and by the question) I assume you mean
$$\frac{\frac{3+h}{3 + h - 2} - 3}{h}$$

You can start by simplifying 3 + h - 2.
Next, look at the numerator
$$\frac{3 + h}{3 + h - 2} - 3$$
and write it as a single fraction:
$$\frac{...}{3 + h - 2}$$

Then you have something of the form
$$\frac{a}{b} / c$$
multiply by 1 in the form: b/b which will give you
$$\frac{ab}{b} / (bc) = a / (bc)$$

Thank you that is what I meant.