Simplify (b^2+b-30)/(3b^2+18b)

$\frac{b^{2} + b - 30}{3 b^{2} + 18 b}$

Step 1

Factor $b^{2} + b - 30$ 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 $- 30$ and whose sum is $1$ .

$- 5, 6$

Write the factored form using these integers.

$\frac{(b - 5) (b + 6)}{3 b^{2} + 18 b}$

Step 2

Simplify terms.

Factor $3 b$ out of $3 b^{2} + 18 b$ .

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

$\frac{(b - 5) (b + 6)}{3 b (b) + 18 b}$

Factor $3 b$ out of $18 b$ .

$\frac{(b - 5) (b + 6)}{3 b (b) + 3 b (6)}$

Factor $3 b$ out of $3 b (b) + 3 b (6)$ .

$\frac{(b - 5) (b + 6)}{3 b (b + 6)}$

Cancel the common factor of $b + 6$ .

Cancel the common factor.

$\frac{(b - 5) (b + 6)}{3 b (b + 6)}$

Rewrite the expression.

$\frac{b - 5}{3 b}$

Simplify (b^2+b-30)/(3b^2+18b)

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