Question

Ex press ri anx in simplest for

Answer 1

Given, $\frac{n}{n-6}+\frac{n+3}{n+9}+\frac{13n+27}{n^2+3n-5n}$

= $\frac{n}{n-6}+\frac{n+3}{n+9}+\frac{13n+27}{n^2-2n}$

= $\frac{n(n+9)}{(n-6)(n+9)}+\frac{(n+3)(n-6)}{(n+9)(n-6)}+\frac{13n+27}{n^2-2n}$

= $\frac{n(n+9)+(n+3)(n-6)}{(n+9)(n-6)}+\frac{13n+27}{n^2-2n}$

= $\frac{n^2+9n+n^2-3n-18}{(n+9)(n-6)}+\frac{13n+27}{n(n-2)}$

= $\frac{2n^2+6n-18}{(n+9)(n-6)}+\frac{13n+27}{n(n-2)}$

= $\frac{(2n^2+6n-18)n(n-2)}{(n+9)(n-6)n(n-2)}+\frac{(13n+27)(n+9)(n-6)}{n(n-2)(n-6)(n+9)}$

= $\frac{2n^4+6n^3-22n^2-12n+36}{(n+9)(n-6)n(n-2)}+\frac{13n^3+66n^2-621n-1458}{n(n-2)(n-6)(n+9)}$

= $\frac{2n^4+6n^3-22n^2-12n+36+13n^3+66n^2-621n-1458}{n(n-2)(n-6)(n+9)}$

= $\frac{2n^4+19n^3+44n^2-633n-1422}{n(n-2)(n-6)(n+9)}$