Question

showing all your work for problem 1 divide simplify and state the domain and problem 2 multiply simplify and state the domain

Answer 1

$\begin{gathered} \text{ Divide }\frac{x^2-25}{3x}\text{ by (x-5). } \\ \text{Factorise x}^2-25,\text{ we have } \\ =\text{ }\frac{(x-5)(x+5)}{3x}\text{ / (x-5)} \\ =\text{ }\frac{(x-5)(x+5)}{3x}\text{ x }\frac{1}{(x-5)} \\ \\ =\frac{x+5}{3x} \\ \end{gathered}$

The domain of the problem is given as

$(-\infty,\text{ 0) U (0, +}\infty)$