Limit Definition of a Derivative for f(x) = 5/(x - 9)

[calculusderogatory]

Hello. I am taking calculus for the first time but it's been 4+ years since I have taken algebra/pre-calculus. I am 30 attempts deep in this problem and I can't figure it out. There are no resources in the textbook like this question. I hope pictures are okay. I got the first part of the question by following the "similar" problem provided in the homework, but I'm having no luck doing that with the rest of the problem. If anyone could help me with how this problem could be solved I would appreciate it.

 

[stapel]

Try simplifying the numerator explicitly. (I don't see any work done, so I can't tell what you've tried; sorry.)

Given the rational sum:

[imath]\qquad \dfrac{5}{t-9} - \dfrac{5}{x-9}[/imath]

...how would you combine these fractions? (Hint: Find a common denominator.) What would the simplified form look like?

When you combine this numerator fraction with the "divided by [imath]t-x = \frac{t-x}{1}"[/imath], what do you get? Once fully simplified, what are the numerator and denominator?

 

[Dr.Peterson]

Hello. I am taking calculus for the first time but it's been 4+ years since I have taken algebra/pre-calculus. I am 30 attempts deep in this problem and I can't figure it out. There are no resources in the textbook like this question. I hope pictures are okay. I got the first part of the question by following the "similar" problem provided in the homework, but I'm having no luck doing that with the rest of the problem. If anyone could help me with how this problem could be solved I would appreciate it. View attachment 36424

In case you need lesson material, here are a couple explanations of simplifying complex fractions:

8.5 Reducing Complex Fractions – Intermediate Algebra

opentextbc.ca

Complex Fractions - MathBitsNotebook(A2)

 

[calculusderogatory]

Try simplifying the numerator explicitly. (I don't see any work done, so I can't tell what you've tried; sorry.)

Given the rational sum:

[imath]\qquad \dfrac{5}{t-9} - \dfrac{5}{x-9}[/imath]

...how would you combine these fractions? (Hint: Find a common denominator.) What would the simplified form look like?

When you combine this numerator fraction with the "divided by [imath]t-x = \frac{t-x}{1}"[/imath], what do you get? Once fully simplified, what are the numerator and denominator?

contrary to my answers in the initial screenshots, it turns out I was on the right track... I was just 30 attempts in because it was showing me that pieces/boxes were wrong just because I hadn't answered the rest of the question yet! So it was telling me the correct denominator was incorrect, causing me to doubt everything I've ever learned! yippee!