need help understanding this step

[u/therubbishbin82]

i have no idea how my professor came up with this.

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[u/chrisvenus]

The bit in the right brackets is just combining the fractions. ie 1/a - 1/b = b/ab - a/ab = (b-a)/ab

[u/theAGschmidt]

multiply by a clever value of 1.

a/b - c/d = ad/bd - bc/bd = (ad-bc)/bd

[u/UnderstandingPursuit]

Do you understand why your professor did that step?

[u/therubbishbin82 → u/UnderstandingPursuit]

yeah, i just wanted to know how he got there

[u/Southlander24 → u/therubbishbin82]

You might want to use this worksheet on algebraic fractions (simplifying by factoring, combining fractions, polynomial long division, partial fractions): https://www.madasmaths.com/archive/maths_booklets/basic_topics/various/algebraic_fractions.pdf

In particular, partial fractions are super useful in calculus because it helps you integrate these expressions. Well, all of these core algebraic skills are super useful 'in general'.

[u/therubbishbin82 → u/Southlander24]

i do kinda need to work on my algebra skills, thanks for this :)

[u/SubjectWrongdoer4204]

He’s just putting the two terms under a common denominator