Could someone please explain this problem to me?

I will show you what I have so far.
Perform the indicated operations and simplify.
w-2/w-7-w+1/w+7+w-77/w^2-49
I made it to this step and now I can't figure out what to do next.
w^2+w-14/(w+7)(w-7) + w^2-6w-7/(w+7)(w-7) + w-77/(w+7)(w-7)=(w^2+w-14)+(w^2-6w-7)+(w-77)/(w+7)(w-7)= 4w-98/(w+7)(w-7).
This is where I'm lost at. I can't seem to figure out the end result.
Thanks for the help.

Only after looking at your solution was I able to figure that your really meant....

(w-2)/(w-7) - (w+1)/(w+7) + (w-77)/(w^2-49)

= [(w^2 + 5w - 14) - (w^2 - 6w - 7) + w-77 ]/[(w+7)(w-7)]

= (12w - 84)/[(w+7)(w-7)]
= 12(w-7)/[(w+7)(w-7)]
= 12/(w+7) , w ≠ 7 (or else we divided by zero)

Thanks but I figured out where I made my mistake and got the answer.

Sure! Let's break down the problem step by step.

The given expression is:
(w - 2)/(w - 7) - (w + 1)/(w + 7) + (w - 77)/(w^2 - 49)

First, let's simplify the denominators w^2 - 49 and convert them using the difference of squares formula:
w^2 - 49 = (w - 7)(w + 7)

Now, we can rewrite the expression as:
(w - 2)/(w - 7) - (w + 1)/(w + 7) + (w - 77)/[(w - 7)(w + 7)]

To combine these fractions, we need to find a common denominator for all three terms. In this case, the common denominator is (w - 7)(w + 7).

Now, let's find the common denominator for the numerators:
(w - 2)(w + 7) - (w + 1)(w - 7) + (w - 77)

Expanding these terms, we get:
(w^2 + 5w - 14) - (w^2 - 6w - 7) + w - 77

Simplifying further, we have:
w^2 + 5w - 14 - w^2 + 6w + 7 + w - 77

Now, let's combine like terms:
(5w + 6w + w) + (-14 + 7 - 77)

Simplifying this further:
12w - 84

Finally, the simplified expression is:
12w - 84 / (w - 7)(w + 7)

Therefore, the end result is 12w - 84 / (w - 7)(w + 7).

I hope this explanation helps you understand the problem and how to solve it. Let me know if you have any further questions!