Simplify (x^2-7x+10)/(2x^5)*(6x^3)/(3x-15)

$\frac{x^{2} - 7 x + 10}{2 x^{5}} \cdot \frac{6 x^{3}}{3 x - 15}$

Factor $x^{2} - 7 x + 10$ 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 $- 7$ .

$- 5, - 2$

Write the factored form using these integers.

$\frac{(x - 5) (x - 2)}{2 x^{5}} \cdot \frac{6 x^{3}}{3 x - 15}$

Simplify terms.

Factor $3$ out of $3 x - 15$ .

Factor $3$ out of $3 x$ .

$\frac{(x - 5) (x - 2)}{2 x^{5}} \cdot \frac{6 x^{3}}{3 (x) - 15}$

Factor $3$ out of $- 15$ .

$\frac{(x - 5) (x - 2)}{2 x^{5}} \cdot \frac{6 x^{3}}{3 x + 3 \cdot - 5}$

Factor $3$ out of $3 x + 3 \cdot - 5$ .

$\frac{(x - 5) (x - 2)}{2 x^{5}} \cdot \frac{6 x^{3}}{3 (x - 5)}$

Combine.

$\frac{(x - 5) (x - 2) (6 x^{3})}{2 x^{5} (3 (x - 5))}$

Cancel the common factor of $x - 5$ .

Cancel the common factor.

$\frac{(x - 5) (x - 2) (6 x^{3})}{2 x^{5} (3 (x - 5))}$

Rewrite the expression.

$\frac{(x - 2) (6 x^{3})}{2 x^{5} \cdot (3)}$

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $(x - 2) (6 x^{3})$ .

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

Cancel the common factors.

Factor $2$ out of $2 x^{5} \cdot (3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{(x - 2) (x^{3})}{x^{5}}$

Cancel the common factor of $x^{3}$ and $x^{5}$ .

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

$\frac{x^{3} (x - 2)}{x^{5}}$

Cancel the common factors.

Factor $x^{3}$ out of $x^{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - 2}{x^{2}}$

Simplify (x^2-7x+10)/(2x^5)*(6x^3)/(3x-15)

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