Simplify Expression

If x>0, simplify the expression below   sqrt((x)/(1-(x-1)/(x)))

Solution

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IN the denominator of the complex fraction, the Least common denominator is X:

1 – (x-1)/x =

(x-(x-1))/ x =

(x – x +1)/x =

1/x

SInce the 1/x is in the denominator, it flips over and x goes into the numerator:

the function becomes x* sqrt(x)