Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

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

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Step 1.1.1.1

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

$x y - \frac{4 x^{5}}{x \cdot x - x y}$

Step 1.1.1.2

Factor $x$ out of $- x y$ .

$x y - \frac{4 x^{5}}{x \cdot x + x (- 1 y)}$

Step 1.1.1.3

Factor $x$ out of $x \cdot x + x (- 1 y)$ .

$x y - \frac{4 x^{5}}{x (x - 1 y)}$

Step 1.1.2

Rewrite $- 1 y$ as $- y$ .

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

Step 1.2

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

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Step 1.2.1

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

$x y - \frac{x (4 x^{4})}{x (x - y)}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Cancel the common factor.

$x y - \frac{x (4 x^{4})}{x (x - y)}$

Step 1.2.2.2

Rewrite the expression.

$x y - \frac{4 x^{4}}{x - y}$

Step 2

To write $x y$ as a fraction with a common denominator, multiply by $\frac{x - y}{x - y}$ .

$\frac{x y (x - y)}{x - y} - \frac{4 x^{4}}{x - y}$

Step 3

Combine the numerators over the common denominator.

$\frac{x y (x - y) - 4 x^{4}}{x - y}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $x$ out of $x y (x - y) - 4 x^{4}$ .

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Step 4.1.1

Factor $x$ out of $x y (x - y)$ .

$\frac{x (y (x - y)) - 4 x^{4}}{x - y}$

Step 4.1.2

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

$\frac{x (y (x - y)) + x (- 4 x^{3})}{x - y}$

Step 4.1.3

Factor $x$ out of $x (y (x - y)) + x (- 4 x^{3})$ .

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

Step 4.2

Apply the distributive property.

$\frac{x (y x + y (- y) - 4 x^{3})}{x - y}$

Step 4.3

Rewrite using the commutative property of multiplication.

$\frac{x (y x - y \cdot y - 4 x^{3})}{x - y}$

Step 4.4

Multiply $y$ by $y$ by adding the exponents.

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Step 4.4.1

Move $y$ .

$\frac{x (y x - (y \cdot y) - 4 x^{3})}{x - y}$

Step 4.4.2

Multiply $y$ by $y$ .

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