#1**+1 **

\(\frac{x-1}{{x}^{2}-16}+\frac{x-4}{1-x}\)

factorise;

\(\frac{x-1}{(x+4)(x-4)}+\frac{x-4}{1-x}\)

times the right hand fraction by \(\frac{(x+4)(x-4)}{(x+4)(x-4)}\)

\(\frac{x-1}{(x+4)(x-4)}+\frac{(x-4)(x+4)(x-4)}{(1-x)(x-4)(x+4)}\)

times the left hand fraction by \(\frac{1-x}{1-x}\)

\(\frac{(x-1)(x-1)}{(x+4)(x-4)(x-1)}+\frac{(x-4)(x+4)(x-4)}{(1-x)(x-4)(x+4)}\)

now that they have the same base we can add them

\(\frac{(x-4)(x+4)(x-4)+(x-1)(x-1)}{(1-x)(x-4)(x+4)}\)

times out the brackets

\(\frac{(x^3-4x^2-16x+64)+(-x^2+2x-1)}{(1-x)(x-4)(x+4)}\)

simplify

\(\frac{x^3-5x^2-14x+63}{(1-x)(x-4)(x+4)}\)

thats as far as it goes im afraid - at least what you wrote

wombat Jun 21, 2017