QC and DI strategy guide

[atirpetkar10]

Hi Tommy and team,

on page 48 in QC and DI strategy guide, we are presented with a problem...
x>0
Quantity A Quantity B

(2+2/(3x))/2 (3+3/(2x))/3

is the below method valid which brings the same answer i.e quantity b is greater

step 1) cross multiply the denominator

6+2/x 6+3/x

step 2) subtract 9 from both sides

2/x 3/x

step 3)since x>0.....therefore (1/x)>o...therefore dividing on both sides by 1/x

2 3

which shows that quantity b is greater as required...
my doubt is whether step 1 and 2 legit?and in case it is correct, do they have any limitations?which i should lookout for before blindly using these steps?

Please let me know.....

Thanks,
Atir

[tommywallach]

Hey Atir,

I can't totally follow your logic here, to be honest. BUT, because x>0, we are totally safe to cross-multiply column A and column B and simplify from there. However, there's no such thing as "cross-multiplying the denominator." That's not a real thing. Cross-multiplication only happens ACROSS an equal or inequality sign, and you're multiplying denominators by numerators, not somehow multiplying JUST denominators.

-t