Simplify (10v-5v^2)/(v^2-11v+18)*(v^2-8v-9)/(15v)

$\frac{10 v - 5 v^{2}}{v^{2} - 11 v + 18} \cdot \frac{v^{2} - 8 v - 9}{15 v}$

Factor $5 v$ out of $10 v - 5 v^{2}$ .

Factor $5 v$ out of $10 v$ .

$\frac{5 v (2) - 5 v^{2}}{v^{2} - 11 v + 18} \cdot \frac{v^{2} - 8 v - 9}{15 v}$

Factor $5 v$ out of $- 5 v^{2}$ .

$\frac{5 v (2) + 5 v (- v)}{v^{2} - 11 v + 18} \cdot \frac{v^{2} - 8 v - 9}{15 v}$

Factor $5 v$ out of $5 v (2) + 5 v (- v)$ .

$\frac{5 v (2 - v)}{v^{2} - 11 v + 18} \cdot \frac{v^{2} - 8 v - 9}{15 v}$

Factor $v^{2} - 11 v + 18$ 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 $- 11$ .

$- 9, - 2$

Write the factored form using these integers.

$\frac{5 v (2 - v)}{(v - 9) (v - 2)} \cdot \frac{v^{2} - 8 v - 9}{15 v}$

Factor $v^{2} - 8 v - 9$ 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 $- 9$ and whose sum is $- 8$ .

$- 9, 1$

Write the factored form using these integers.

$\frac{5 v (2 - v)}{(v - 9) (v - 2)} \cdot \frac{(v - 9) (v + 1)}{15 v}$

Simplify terms.

Cancel the common factor of $5 v$ .

Factor $5 v$ out of $15 v$ .

$\frac{5 v (2 - v)}{(v - 9) (v - 2)} \cdot \frac{(v - 9) (v + 1)}{5 v (3)}$

Cancel the common factor.

$\frac{5 v (2 - v)}{(v - 9) (v - 2)} \cdot \frac{(v - 9) (v + 1)}{5 v \cdot 3}$

Rewrite the expression.

$\frac{2 - v}{(v - 9) (v - 2)} \cdot \frac{(v - 9) (v + 1)}{3}$

Cancel the common factor of $v - 9$ .

Cancel the common factor.

$\frac{2 - v}{(v - 9) (v - 2)} \cdot \frac{(v - 9) (v + 1)}{3}$

Rewrite the expression.

$\frac{2 - v}{v - 2} \cdot \frac{v + 1}{3}$

Multiply $\frac{2 - v}{v - 2}$ by $\frac{v + 1}{3}$ .

$\frac{(2 - v) (v + 1)}{(v - 2) \cdot 3}$

Cancel the common factor of $2 - v$ and $v - 2$ .

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{(- 1 (- 2) - v) (v + 1)}{(v - 2) \cdot 3}$

Factor $- 1$ out of $- v$ .

$\frac{(- 1 (- 2) - (v)) (v + 1)}{(v - 2) \cdot 3}$

Factor $- 1$ out of $- 1 (- 2) - (v)$ .

$\frac{- 1 (- 2 + v) (v + 1)}{(v - 2) \cdot 3}$

Reorder terms.

$\frac{- 1 (v - 2) (v + 1)}{(v - 2) \cdot 3}$

Cancel the common factor.

$\frac{- 1 (v - 2) (v + 1)}{(v - 2) \cdot 3}$

Rewrite the expression.

$\frac{- 1 (v + 1)}{3}$

Move the negative in front of the fraction.

$- \frac{v + 1}{3}$

Simplify (10v-5v^2)/(v^2-11v+18)*(v^2-8v-9)/(15v)

Related Questions

Support LCMGCF.com by disabling your adblocker.