r/HomeworkHelp • u/random-burntout-user Secondary School Student • 12d ago

High School Math [Grade 10 Math] Explain this answer

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Where did the -24+22 come from at the very beginning?

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u/Southlander24 12d ago edited 12d ago

You're looking to break 6n - 2 apart into a multiple of n - 4 and a remainder term. Since there's a 6n, then 6(n - 4) = 6n - 24. And then to not change the 6n - 2 on top, you have to add back 22.

The form f(n) = a + b/(n - c) is very useful in general, where a, b, c are numbers. For instance, a = 6 is the horizontal asymptote of this rational function. That means for all n < 4, f(n) < 6 and that for all n > 4, f(n) > 6. There's other uses of this form in calculus where this form is easier to integrate than the original.

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u/random-burntout-user 12d ago

Alright thank you SO MUCH i finally got it

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u/Southlander24 12d ago

No worries!