To simplify the given complex fraction `(16/(x-2))/(4/(x+1)+6/x)` , we may look for the LCD or least common denominator.
The denominators are `(x-2)` , `x` , and `(x+1)` . All are distinct factors.
Thus, we get the LCD by getting the product of the distinct factors from denominator side of each term.
`LCD =(x-2)*x* (x+1)`
Maintain the factored form of the LCD for easier cancellation of common factors on each term.
Multiply each term by the...
To simplify the given complex fraction `(16/(x-2))/(4/(x+1)+6/x)` , we may look for the LCD or least common denominator.
The denominators are `(x-2)` , `x` , and `(x+1)` . All are distinct factors.
Thus, we get the LCD by getting the product of the distinct factors from denominator side of each term.
`LCD =(x-2)*x* (x+1)`
Maintain the factored form of the LCD for easier cancellation of common factors on each term.
Multiply each term by the LCD=(x-2)*x* (x+1).
`(16/(x-2)*(x-2)*x* (x+1))/(4/(x+1)*(x-2)*x* (x+1)+6/x*(x-2)*x* (x+1))`
`(16*x* (x+1))/(4*(x-2)*x +6*(x-2)* (x+1))`
Apply distributive property.
`(16x*(x+1))/((4x-8)*x +(6x-12)* (x+1))`
`(16x^2+16x)/((4x^2-8x) +(6x^2+6x-12x-12))`
Combine possible like terms.
`(16x^2+16x)/((4x^2-8x) +(6x^2-6x-12))`
`(16x^2+16x)/(4x^2-8x+6x^2-6x-12)`
`(16x^2+16x)/(10x^2-14x-12)`
Factor out 2 from each side.
`(2(8x^2+8x))/(2(5x^2-7x-6))`
Cancel out common factor `2` .
`(8x^2+8x)/(5x^2-7x-6)`
The complex fraction `(16/(x-2))/(4/(x+1)+6/x)` simplifies to `(8x^2+8x)/(5x^2-7x-6)` .
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