Mathematics: Given f(x)=3x^2+9x and g(x)=x^2-x-12, find (f/g)(x).

Given f(x)=3x^2+9x and g(x)=x^2-x-12, find (f/g)(x). - id3292125413537, melissaschnelting

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20.01.2022

$\frac{f}{g}(x) = 3\frac{x}{(x-4)}$

Step-by-step explanation:

We have, $f(x) = 3x^{2} + 9x$ and $g(x) = x^{2} -x-12$ . We need to find $\frac{f}{g} (x) = \frac{f(x)}{g(x)}$

⇒ $\frac{f}{g} (x) = \frac{f(x)}{g(x)}$

⇒ $\frac{f(x)}{g(x)} = \frac{3x^{2}+9x}{x^{2}-x-12}$

⇒ $\frac{f(x)}{g(x)} = \frac{3x^{2}+9x}{(x+3)(x-4)}$

⇒ $\frac{f(x)}{g(x)} = \frac{3x(x+3)}{(x+3)(x-4)}$

⇒ $\frac{f(x)}{g(x)} = \frac{3x}{(x-4)}$

⇒ $\frac{f(x)}{g(x)} = 3\frac{x}{(x-4)}$

⇒ $\frac{f}{g}(x) = 3\frac{x}{(x-4)}$

Hence , $\frac{f}{g}(x) = 3\frac{x}{(x-4)}$ .

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