Find the Quotient of the Two Functions f(x)=5x^2-9x , g(x)=x^2-4x-45

$f (x) = 5 x^{2} - 9 x$ , $g (x) = x^{2} - 4 x - 45$

Step 1

Replace the function designators with the actual functions in $\frac{f (x)}{g (x)}$ .

$\frac{5 x^{2} - 9 x}{x^{2} - 4 x - 45}$

Step 2

Simplify.

Factor $x$ out of $5 x^{2} - 9 x$ .

Factor $x$ out of $5 x^{2}$ .

$\frac{x (5 x) - 9 x}{x^{2} - 4 x - 45}$

Factor $x$ out of $- 9 x$ .

$\frac{x (5 x) + x \cdot - 9}{x^{2} - 4 x - 45}$

Factor $x$ out of $x (5 x) + x \cdot - 9$ .

$\frac{x (5 x - 9)}{x^{2} - 4 x - 45}$

Factor $x^{2} - 4 x - 45$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 45$ and whose sum is $- 4$ .

$- 9, 5$

Write the factored form using these integers.

$\frac{x (5 x - 9)}{(x - 9) (x + 5)}$

Find the Quotient of the Two Functions f(x)=5x^2-9x , g(x)=x^2-4x-45

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