Algebra Examples

$\frac{5}{12 x^{4} y} - \frac{1}{5 x^{2} y^{3}}$

Step 1

To write $\frac{5}{12 x^{4} y}$ as a fraction with a common denominator, multiply by $\frac{5 y^{2}}{5 y^{2}}$ .

$\frac{5}{12 x^{4} y} \cdot \frac{5 y^{2}}{5 y^{2}} - \frac{1}{5 x^{2} y^{3}}$

Step 2

To write $- \frac{1}{5 x^{2} y^{3}}$ as a fraction with a common denominator, multiply by $\frac{12 x^{2}}{12 x^{2}}$ .

$\frac{5}{12 x^{4} y} \cdot \frac{5 y^{2}}{5 y^{2}} - \frac{1}{5 x^{2} y^{3}} \cdot \frac{12 x^{2}}{12 x^{2}}$

Step 3

Write each expression with a common denominator of $60 x^{4} y^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{12 x^{4} y}$ by $\frac{5 y^{2}}{5 y^{2}}$ .

$\frac{5 (5 y^{2})}{12 x^{4} y (5 y^{2})} - \frac{1}{5 x^{2} y^{3}} \cdot \frac{12 x^{2}}{12 x^{2}}$

Step 3.2

Multiply $5$ by $12$ .

$\frac{5 (5 y^{2})}{60 x^{4} y \cdot y^{2}} - \frac{1}{5 x^{2} y^{3}} \cdot \frac{12 x^{2}}{12 x^{2}}$

Step 3.3

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 3.3.1

Move $y^{2}$ .

$\frac{5 (5 y^{2})}{60 x^{4} (y^{2} y)} - \frac{1}{5 x^{2} y^{3}} \cdot \frac{12 x^{2}}{12 x^{2}}$

Step 3.3.2

Multiply $y^{2}$ by $y$ .

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Step 3.3.2.1

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

$\frac{5 (5 y^{2})}{60 x^{4} (y^{2} y^{1})} - \frac{1}{5 x^{2} y^{3}} \cdot \frac{12 x^{2}}{12 x^{2}}$

Step 3.3.2.2

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

$\frac{5 (5 y^{2})}{60 x^{4} y^{2 + 1}} - \frac{1}{5 x^{2} y^{3}} \cdot \frac{12 x^{2}}{12 x^{2}}$

Step 3.3.3

Add $2$ and $1$ .

$\frac{5 (5 y^{2})}{60 x^{4} y^{3}} - \frac{1}{5 x^{2} y^{3}} \cdot \frac{12 x^{2}}{12 x^{2}}$

Step 3.4

Multiply $\frac{1}{5 x^{2} y^{3}}$ by $\frac{12 x^{2}}{12 x^{2}}$ .

$\frac{5 (5 y^{2})}{60 x^{4} y^{3}} - \frac{12 x^{2}}{5 x^{2} y^{3} (12 x^{2})}$

Step 3.5

Multiply $12$ by $5$ .

$\frac{5 (5 y^{2})}{60 x^{4} y^{3}} - \frac{12 x^{2}}{60 x^{2} y^{3} x^{2}}$

Step 3.6

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 3.6.1

Move $x^{2}$ .

$\frac{5 (5 y^{2})}{60 x^{4} y^{3}} - \frac{12 x^{2}}{60 (x^{2} x^{2}) y^{3}}$

Step 3.6.2

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

$\frac{5 (5 y^{2})}{60 x^{4} y^{3}} - \frac{12 x^{2}}{60 x^{2 + 2} y^{3}}$

Step 3.6.3

Add $2$ and $2$ .

$\frac{5 (5 y^{2})}{60 x^{4} y^{3}} - \frac{12 x^{2}}{60 x^{4} y^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (5 y^{2}) - 12 x^{2}}{60 x^{4} y^{3}}$

Step 5

Multiply $5$ by $5$ .

$\frac{25 y^{2} - 12 x^{2}}{60 x^{4} y^{3}}$