Simplify (6x^3-10x^2)/(3x^3-2x^2-5x)

$\frac{6 x^{3} - 10 x^{2}}{3 x^{3} - 2 x^{2} - 5 x}$

Step 1

Factor $2 x^{2}$ out of $6 x^{3} - 10 x^{2}$ .

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

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

Factor $2 x^{2}$ out of $- 10 x^{2}$ .

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

Factor $2 x^{2}$ out of $2 x^{2} (3 x) + 2 x^{2} (- 5)$ .

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

Step 2

Simplify the denominator.

Factor $x$ out of $3 x^{3} - 2 x^{2} - 5 x$ .

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

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

Factor $x$ out of $- 2 x^{2}$ .

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

Factor $x$ out of $- 5 x$ .

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

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

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

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

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

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 5 = - 15$ and whose sum is $b = - 2$ .

Factor $- 2$ out of $- 2 x$ .

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

Rewrite $- 2$ as $3$ plus $- 5$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

$\frac{2 x^{2} (3 x - 5)}{x (3 x (x + 1) - 5 (x + 1))}$

Factor the polynomial by factoring out the greatest common factor, $x + 1$ .

$\frac{2 x^{2} (3 x - 5)}{x ((x + 1) (3 x - 5))}$

$\frac{2 x^{2} (3 x - 5)}{x (x + 1) (3 x - 5)}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{2}$ and $x$ .

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

$\frac{x (2 x (3 x - 5))}{x (x + 1) (3 x - 5)}$

Cancel the common factors.

Factor $x$ out of $x (x + 1) (3 x - 5)$ .

$\frac{x (2 x (3 x - 5))}{x ((x + 1) (3 x - 5))}$

Cancel the common factor.

$\frac{x (2 x (3 x - 5))}{x ((x + 1) (3 x - 5))}$

Rewrite the expression.

$\frac{2 x (3 x - 5)}{(x + 1) (3 x - 5)}$

Cancel the common factor of $3 x - 5$ .

Cancel the common factor.

$\frac{2 x (3 x - 5)}{(x + 1) (3 x - 5)}$

Rewrite the expression.

$\frac{2 x}{x + 1}$

Simplify (6x^3-10x^2)/(3x^3-2x^2-5x)

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