`(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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