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(x-1/x^2-16)+(x-4/1-x) got a quiz rn need of help

Guest Jun 21, 2017
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$$\frac{x-1}{{x}^{2}-16}+\frac{x-4}{1-x}$$

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