`(15-2/x)/(x/5+4)` Simplify the complex fraction.

Expert Answers

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To simplify the given complex fraction `(15-2/x)/(x/5+4)` , we may look for the LCD or least common denominator.

The denominators are `x` and `5` . Both are distinct factors.

Thus, we get the LCD by getting the product of the distinct factors from denominator side of each term.

`LCD =5*x=5x`

Multiply each term by the `LCD=5x` .

`(15*5x-2/x*5x)/(x/5*5x+4*5x)`

`(75x-10)/(x^2+20x)`

Another method is to simplify top and bottom as single fraction.

Let `15= (15x)/x` and `4 =20/5` .

`(15-2/x)/(x/5+4)`

`((15x)/x-2/x)/(x/5+20/5)`

`((15x-2)/x)/((x+20)/5)`

Flip the fraction at the bottom to proceed to multiplication.

`((15x-2)/x)* (5/(x+20))`

Multiply across fractions.

`((15x-2)*5)/(x*(x+20x))`

`(75x-10)/(x^2+20x)`

 The complex fraction `(15-2/x)/(x/5+4)`  simplifies to `(75x-10)/(x^2+20x)` .

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