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

1 Answer
Mar 9, 2018

1/5

Explanation:

(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