Simplify (k+8)/(k^2-2k-80)*(k^2-6k-40)/(5k)

$\frac{k + 8}{k^{2} - 2 k - 80} \cdot \frac{k^{2} - 6 k - 40}{5 k}$

Factor $k^{2} - 2 k - 80$ 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 $- 80$ and whose sum is $- 2$ .

$- 10, 8$

Write the factored form using these integers.

$\frac{k + 8}{(k - 10) (k + 8)} \cdot \frac{k^{2} - 6 k - 40}{5 k}$

Factor $k^{2} - 6 k - 40$ 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 $- 40$ and whose sum is $- 6$ .

$- 10, 4$

Write the factored form using these integers.

$\frac{k + 8}{(k - 10) (k + 8)} \cdot \frac{(k - 10) (k + 4)}{5 k}$

Simplify terms.

Cancel the common factor of $k - 10$ .

Cancel the common factor.

$\frac{k + 8}{(k - 10) (k + 8)} \cdot \frac{(k - 10) (k + 4)}{5 k}$

Rewrite the expression.

$\frac{k + 8}{k + 8} \cdot \frac{k + 4}{5 k}$

Multiply $\frac{k + 8}{k + 8}$ by $\frac{k + 4}{5 k}$ .

$\frac{(k + 8) (k + 4)}{(k + 8) (5 k)}$

Cancel the common factor of $k + 8$ .

Cancel the common factor.

$\frac{(k + 8) (k + 4)}{(k + 8) (5 k)}$

Rewrite the expression.

$\frac{k + 4}{5 k}$

Simplify (k+8)/(k^2-2k-80)*(k^2-6k-40)/(5k)

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