Simplify (x^3-3x^2)/(4x^2-5x)

$\frac{x^{3} - 3 x^{2}}{4 x^{2} - 5 x}$

Step 1

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

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

$\frac{x^{2} x - 3 x^{2}}{4 x^{2} - 5 x}$

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

$\frac{x^{2} x + x^{2} \cdot - 3}{4 x^{2} - 5 x}$

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

$\frac{x^{2} (x - 3)}{4 x^{2} - 5 x}$

$\frac{x^{2} (x - 3)}{4 x^{2} - 5 x}$

Step 2

Factor $x$ out of $4 x^{2} - 5 x$ .

Factor $x$ out of $4 x^{2}$ .

$\frac{x^{2} (x - 3)}{x (4 x) - 5 x}$

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

$\frac{x^{2} (x - 3)}{x (4 x) + x \cdot - 5}$

Factor $x$ out of $x (4 x) + x \cdot - 5$ .

$\frac{x^{2} (x - 3)}{x (4 x - 5)}$

$\frac{x^{2} (x - 3)}{x (4 x - 5)}$

Step 3

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

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

$\frac{x (x (x - 3))}{x (4 x - 5)}$

Cancel the common factors.

Cancel the common factor.

$\frac{x (x (x - 3))}{x (4 x - 5)}$

Rewrite the expression.

$\frac{x (x - 3)}{4 x - 5}$

$\frac{x (x - 3)}{4 x - 5}$

$\frac{x (x - 3)}{4 x - 5}$

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