Finite Math Examples

$\frac{8 x^{3 y}}{20 x^{2} y^{2}} = \frac{2 x}{5 y}$

Step 1

Subtract $\frac{2 x}{5 y}$ from both sides of the equation.

$\frac{8 x^{3 y}}{20 x^{2} y^{2}} - \frac{2 x}{5 y} = 0$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $8$ and $20$ .

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Step 2.1.1

Factor $4$ out of $8 x^{3 y}$ .

$\frac{4 (2 x^{3 y})}{20 x^{2} y^{2}} - \frac{2 x}{5 y} = 0$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $4$ out of $20 x^{2} y^{2}$ .

$\frac{4 (2 x^{3 y})}{4 (5 x^{2} y^{2})} - \frac{2 x}{5 y} = 0$

Step 2.1.2.2

Cancel the common factor.

$\frac{4 (2 x^{3 y})}{4 (5 x^{2} y^{2})} - \frac{2 x}{5 y} = 0$

Step 2.1.2.3

Rewrite the expression.

$\frac{2 x^{3 y}}{5 x^{2} y^{2}} - \frac{2 x}{5 y} = 0$

Step 2.2

Cancel the common factor of $x^{3 y}$ and $x^{2}$ .

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Step 2.2.1

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

$\frac{x^{2} (2 x^{3 y - 2})}{5 x^{2} y^{2}} - \frac{2 x}{5 y} = 0$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $x^{2}$ out of $5 x^{2} y^{2}$ .

$\frac{x^{2} (2 x^{3 y - 2})}{x^{2} (5 y^{2})} - \frac{2 x}{5 y} = 0$

Step 2.2.2.2

Cancel the common factor.

$\frac{x^{2} (2 x^{3 y - 2})}{x^{2} (5 y^{2})} - \frac{2 x}{5 y} = 0$

Step 2.2.2.3

Rewrite the expression.

$\frac{2 x^{3 y - 2}}{5 y^{2}} - \frac{2 x}{5 y} = 0$

Step 3

To write $- \frac{2 x}{5 y}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{2 x^{3 y - 2}}{5 y^{2}} - \frac{2 x}{5 y} \cdot \frac{y}{y} = 0$

Step 4

Write each expression with a common denominator of $5 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2 x}{5 y}$ by $\frac{y}{y}$ .

$\frac{2 x^{3 y - 2}}{5 y^{2}} - \frac{2 x y}{5 y \cdot y} = 0$

Step 4.2

Raise $y$ to the power of $1$ .

$\frac{2 x^{3 y - 2}}{5 y^{2}} - \frac{2 x y}{5 (y^{1} y)} = 0$

Step 4.3

Raise $y$ to the power of $1$ .

$\frac{2 x^{3 y - 2}}{5 y^{2}} - \frac{2 x y}{5 (y^{1} y^{1})} = 0$

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 x^{3 y - 2}}{5 y^{2}} - \frac{2 x y}{5 y^{1 + 1}} = 0$

Step 4.5

Add $1$ and $1$ .

$\frac{2 x^{3 y - 2}}{5 y^{2}} - \frac{2 x y}{5 y^{2}} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{2 x^{3 y - 2} - 2 x y}{5 y^{2}} = 0$

Step 6

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

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Step 6.1

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

$\frac{2 (x^{3 y - 2}) - 2 x y}{5 y^{2}} = 0$

Step 6.2

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

$\frac{2 (x^{3 y - 2}) + 2 (- x y)}{5 y^{2}} = 0$

Step 6.3

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

$\frac{2 (x^{3 y - 2} - x y)}{5 y^{2}} = 0$