How do you simplify #\frac { \frac { 1} { 5} - \frac { 1} { a } } { \frac { a - 5} { a } }#?

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Answer 1 · 2018-03-09T06:32:47

#1/5#

#(1/5-1/a)/((a-5)/a)#

Change the fractions in the numerator to have common denominators:

#(a/(5a)-5/(5a))/((a-5)/a)#

Subtract the fractions in the numerator:

#((a-5)/(5a))/((a-5)/a)#

Divide the numerator by the denominator using keep-change-flip (i.e. #(1/x)/(1/y) = (1/x)*(y/1) = y/x#)

#(a-5)/((5a))*((a)/(a-5))#

#a/(5a)#

#1/5#