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

Expert Answers

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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` .



Another method is to simplify top and bottom as single fraction. Let `6=18/3` and `10=(10x)/x` .


`(x/3-18/3)/((10x)/x+4/x) `


Flip the fraction at the bottom to proceed to multiplication.


Multiply across fractions.



The complex fraction `(x/3-6)/(10+4/x)` simplifies to ` (x^2-18x)/(30x+12)` .

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