Simplify (3x^2+21x-54)/(x^2+3x-54)

$\frac{3 x^{2} + 21 x - 54}{x^{2} + 3 x - 54}$

Step 1

Simplify the numerator.

Factor $3$ out of $3 x^{2} + 21 x - 54$ .

Factor $3$ out of $3 x^{2}$ .

$\frac{3 (x^{2}) + 21 x - 54}{x^{2} + 3 x - 54}$

Factor $3$ out of $21 x$ .

$\frac{3 (x^{2}) + 3 (7 x) - 54}{x^{2} + 3 x - 54}$

Factor $3$ out of $- 54$ .

$\frac{3 x^{2} + 3 (7 x) + 3 \cdot - 18}{x^{2} + 3 x - 54}$

Factor $3$ out of $3 x^{2} + 3 (7 x)$ .

$\frac{3 (x^{2} + 7 x) + 3 \cdot - 18}{x^{2} + 3 x - 54}$

Factor $3$ out of $3 (x^{2} + 7 x) + 3 \cdot - 18$ .

$\frac{3 (x^{2} + 7 x - 18)}{x^{2} + 3 x - 54}$

Factor $x^{2} + 7 x - 18$ 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 $- 18$ and whose sum is $7$ .

$- 2, 9$

Write the factored form using these integers.

$\frac{3 ((x - 2) (x + 9))}{x^{2} + 3 x - 54}$

$\frac{3 (x - 2) (x + 9)}{x^{2} + 3 x - 54}$

Step 2

Factor $x^{2} + 3 x - 54$ 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 $- 54$ and whose sum is $3$ .

$- 6, 9$

Write the factored form using these integers.

$\frac{3 (x - 2) (x + 9)}{(x - 6) (x + 9)}$

Step 3

Cancel the common factor of $x + 9$ .

Cancel the common factor.

$\frac{3 (x - 2) (x + 9)}{(x - 6) (x + 9)}$

Rewrite the expression.

$\frac{3 (x - 2)}{x - 6}$

Simplify (3x^2+21x-54)/(x^2+3x-54)

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