Slope of a tangent line

  • #1
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?
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
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By lack of brackets (and by the question) I assume you mean
[tex]\frac{\frac{3+h}{3 + h - 2} - 3}{h}[/tex]

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

Then you have something of the form
[tex]\frac{a}{b} / c[/tex]
multiply by 1 in the form: b/b which will give you
[tex]\frac{ab}{b} / (bc) = a / (bc)[/tex]
 
  • #3
By lack of brackets (and by the question) I assume you mean
[tex]\frac{\frac{3+h}{3 + h - 2} - 3}{h}[/tex]

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

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

Thank you that is what I meant.
 

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