(x/3-6)/(10+4/x) Simplify the complex fraction.

To simplify the given complex fraction (x/3-6)/(10+4/x) , we may look for the LCD or least common denominator.
The denominators are x  and 3 . Both are distinct factors.
Thus, we get the LCD by getting the product of the distinct factors from denominator side of each term.
LCD =3*x=3x
Multiply each term by the LCD=3x .
(x/3*3x-6*3x)/(10*3x+4/x*3x)
(x^2-18x)/(30x+12)
Another method is to simplify top and bottom as single fraction. Let 6=18/3 and 10=(10x)/x .
(x/3-6)/(10+4/x)
(x/3-18/3)/((10x)/x+4/x)
((x-18)/3)/((10x+4)/x)
Flip the fraction at the bottom to proceed to multiplication.
((x-18)/3)*(x/(10x+4))
Multiply across fractions.
((x-18)*x)/(3*(10x+4))
(x^2-18x)/(30x+12)
The complex fraction (x/3-6)/(10+4/x) simplifies to  (x^2-18x)/(30x+12) .

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