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

(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))