`(1/(3x^2-3))/(5/(x+1)-(x+4)/(x^2-3x-4))` Simplify the complex fraction.

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`(1/(3x^2-3))/(5/(x+1)-(x+4)/(x^2-3x-4))`

Let's factorize the denominators of the terms in the complex fraction,

`=(1/(3(x^2-1)))/(5/(x+1)-(x+4)/(x^2+x-4x-4))`

`=(1/(3(x+1)(x-1)))/(5/(x+1)-(x+4)/(x(x+1)-4(x+1)))`

`=(1/(3(x+1)(x-1)))/(5/(x+1)-(x+4)/((x-4)(x+1)))`

LCD for all the denominators in the complex fraction is `(x+1)(x-1)(x-4)`

Multiply both the numerator and denominator of the complex fraction by the LCD,

`=((x+1)(x-1)(x-4)(1/(3(x+1)(x-1))))/((x+1)(x-1)(x-4)(5/(x+1)-(x+4)/((x-4)(x+1))))`  

Use the distributive property in the denominator of the complex fraction,

`=((x-4)/3)/(5(x-1)(x-4)-(x+4)(x-1))`

`=((x-4)/3)/((x-1)(5(x-4)-(x+4)))` 

`=(x-4)/(3(x-1)(5x-20-x-4))`

`=(x-4)/(3(x-1)(4x-24))`

`=(x-4)/(3(x-1)4(x-6))`

`=(x-4)/(12(x-1)(x-6))`

 

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