Question

43n2 - 24n +455n2_- 25n

Answer 1

The expression should first be simplified before they are divided

`\begin{gathered} \frac{4}{3n^2\text{ -24n +45 }}\text{ - }(5)/(5n^2-25n) \\ =\text{ }(4)/(n^2-8n+15)\text{ - }(5)/(5n^2-25n)\text{ ( divide by 3 )} \\ =(4)/((n^2-3n)-(5n+15))\text{ - }\frac{5}{5n\text{ ( n - 5 )}}\text{ ( factorising the denominators )} \\ =\text{ }\frac{4}{n(n-3\text{ ) - 5 (n - 3 )}}\text{ - }\frac{5}{5n\text{ (n-5)}} \\ =\text{ }(4)/((n-3)(n-5))\text{ - }(1)/(n(n-5))\text{ ( 5 cancels 5 )} \\ =\text{ Now we need to make it into a single expression by finding the L.C.M } \\ =\text{ }\frac{4n\text{ - (n-3)}}{n(n-3)(n-5)}\text{ = }\frac{4n-n\text{ +3}}{n(n-3)(n-5)}\text{ = }\frac{3n\text{ +3}}{n(n-3)(n-5)} \\ =\text{ The simpliest form therefore is }(3n+3)/(n(n-3)(n-5)) \\ \end{gathered}`