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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