Given:
[tex]f(x)=x^2-25\text{ and }g(x)=x+5.[/tex]
Required:
[tex]We\text{ need to find }(\frac{f}{g})(x).[/tex]
Explanation:
[tex]We\text{ know that }(\frac{f}{g})(x)=\frac{f(x)}{g(x)}.[/tex]
[tex]Substitute\text{ }f(x)=x^2-25\text{ and }g(x)=x+5\text{ in the equation.}[/tex]
[tex](\frac{f}{g})(x)=\frac{x^2-25}{x+5}[/tex]
[tex](\frac{f}{g})(x)=\frac{x^2-5^2}{x+5}[/tex][tex]Use\text{ }x^2-5^2=(x-5)(x+5).[/tex]
[tex](\frac{f}{g})(x)=\frac{(x-5)(x+5)}{x+5}[/tex]
Cancel out the term (x+5).
[tex](\frac{f}{g})(x)=x-5[/tex]
Final answer:
[tex](\frac{f}{g})(x)=x-5[/tex]
