Simplify (b^2-3b-10)/((b-2)^2)*(b-2)/(b-5)

$\frac{b^{2} - 3 b - 10}{{(b - 2)}^{2}} \cdot \frac{b - 2}{b - 5}$

Step 1

Factor $b^{2} - 3 b - 10$ 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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Write the factored form using these integers.

$\frac{(b - 5) (b + 2)}{{(b - 2)}^{2}} \cdot \frac{b - 2}{b - 5}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $b - 5$ .

Cancel the common factor.

$\frac{(b - 5) (b + 2)}{{(b - 2)}^{2}} \cdot \frac{b - 2}{b - 5}$

Rewrite the expression.

$\frac{b + 2}{{(b - 2)}^{2}} \cdot (b - 2)$

Cancel the common factor of $b - 2$ .

Factor $b - 2$ out of ${(b - 2)}^{2}$ .

$\frac{b + 2}{(b - 2) (b - 2)} \cdot (b - 2)$

Cancel the common factor.

$\frac{b + 2}{(b - 2) (b - 2)} \cdot (b - 2)$

Rewrite the expression.

$\frac{b + 2}{b - 2}$

Simplify (b^2-3b-10)/((b-2)^2)*(b-2)/(b-5)

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