Algebra Examples

$f (x) = 9 x^{2} - 5 x$ , $g (x) = x^{2} - 3 x - 10$

Step 1

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

$\frac{9 x^{2} - 5 x}{x^{2} - 3 x - 10}$

Step 2

Simplify.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

$\frac{x (9 x) - 5 x}{x^{2} - 3 x - 10}$

Step 2.1.2

Factor $x$ out of $- 5 x$ .

$\frac{x (9 x) + x \cdot - 5}{x^{2} - 3 x - 10}$

Step 2.1.3

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

$\frac{x (9 x - 5)}{x^{2} - 3 x - 10}$

Step 2.2

Factor $x^{2} - 3 x - 10$ using the AC method.

Tap for more steps...

Step 2.2.1

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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Step 2.2.2

Write the factored form using these integers.

$\frac{x (9 x - 5)}{(x - 5) (x + 2)}$