algebra exponents and fractionsI could be over thinking or tired... But I am to embarrassed...

Jameson Lucero

Jameson Lucero

Answered

2022-07-07

algebra exponents and fractions
I could be over thinking or tired... But I am to embarrassed to ask my prof. this probably very simple algebra rule I am ignorant of... Also this is just a snip-it from a inductive proof example.
Say you have something like this
4 k 1 3 + 3 4 k 3 =
4 4 k 1 3
My question is what algebra rules or rules of fractions allow this? In other words what computation is going on? I can agree that the 3 should cancel out
3 4 k 3 = 4 k
But wouldn't that mean it be something like this
( 4 k 1 ) 4 k 3
or more accurately
( 4 k 1 ) 3 4 k
and not this?
4 4 k 1 3

Answer & Explanation

jugf5

jugf5

Expert

2022-07-08Added 18 answers

4 k 1 3 + 3 4 k 3  these fractions have the same denominator so we can write the fraction as one now  4 k 1 + 3 4 k 3  recall  u + 3 u = 4 u  so we have  4 k ( 1 + 3 ) 1 3 = 4 k ( 4 ) 1 3 = 4 4 k 1 3 = 4 k + 1 1 3

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