Finite Math Examples

$f (x) = \frac{- 12 x + 27}{- 18 x + 81}$

Step 1

Factor $3$ out of $- 12 x + 27$ .

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Step 1.1

Factor $3$ out of $- 12 x$ .

$f (x) = \frac{3 (- 4 x) + 27}{- 18 x + 81}$

Step 1.2

Factor $3$ out of $27$ .

$f (x) = \frac{3 (- 4 x) + 3 (9)}{- 18 x + 81}$

Step 1.3

Factor $3$ out of $3 (- 4 x) + 3 (9)$ .

$f (x) = \frac{3 (- 4 x + 9)}{- 18 x + 81}$

Step 2

Factor $9$ out of $- 18 x + 81$ .

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Step 2.1

Factor $9$ out of $- 18 x$ .

$f (x) = \frac{3 (- 4 x + 9)}{9 (- 2 x) + 81}$

Step 2.2

Factor $9$ out of $81$ .

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

Step 2.3

Factor $9$ out of $9 (- 2 x) + 9 (9)$ .

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

Step 3

Reduce the expression $\frac{3 (- 4 x + 9)}{9 (- 2 x + 9)}$ by cancelling the common factors.

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Step 3.1

Factor $3$ out of $9 (- 2 x + 9)$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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