Algebra Examples

$\frac{1}{x^{2}} - \frac{3}{2 x y^{3}} + \frac{7}{5 x y}$

Step 1

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

$\frac{1}{x^{2}} \cdot \frac{2 y^{3}}{2 y^{3}} - \frac{3}{2 x y^{3}} + \frac{7}{5 x y}$

Step 2

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

$\frac{1}{x^{2}} \cdot \frac{2 y^{3}}{2 y^{3}} - \frac{3}{2 x y^{3}} \cdot \frac{x}{x} + \frac{7}{5 x y}$

Step 3

Write each expression with a common denominator of $2 x^{2} y^{3}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

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

$\frac{2 y^{3}}{x^{2} (2 y^{3})} - \frac{3}{2 x y^{3}} \cdot \frac{x}{x} + \frac{7}{5 x y}$

Step 3.2

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

$\frac{2 y^{3}}{x^{2} (2 y^{3})} - \frac{3 x}{2 x y^{3} x} + \frac{7}{5 x y}$

Step 3.3

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

$\frac{2 y^{3}}{x^{2} (2 y^{3})} - \frac{3 x}{2 (x^{1} x) y^{3}} + \frac{7}{5 x y}$

Step 3.4

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

$\frac{2 y^{3}}{x^{2} (2 y^{3})} - \frac{3 x}{2 (x^{1} x^{1}) y^{3}} + \frac{7}{5 x y}$

Step 3.5

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

$\frac{2 y^{3}}{x^{2} (2 y^{3})} - \frac{3 x}{2 x^{1 + 1} y^{3}} + \frac{7}{5 x y}$

Step 3.6

Add $1$ and $1$ .

$\frac{2 y^{3}}{x^{2} (2 y^{3})} - \frac{3 x}{2 x^{2} y^{3}} + \frac{7}{5 x y}$

Step 3.7

Reorder the factors of $x^{2} (2 y^{3})$ .

$\frac{2 y^{3}}{2 y^{3} x^{2}} - \frac{3 x}{2 x^{2} y^{3}} + \frac{7}{5 x y}$

Step 3.8

Reorder the factors of $2 x^{2} y^{3}$ .

$\frac{2 y^{3}}{2 y^{3} x^{2}} - \frac{3 x}{2 y^{3} x^{2}} + \frac{7}{5 x y}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 y^{3} - 3 x}{2 y^{3} x^{2}} + \frac{7}{5 x y}$

Step 5

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

$\frac{2 y^{3} - 3 x}{2 y^{3} x^{2}} \cdot \frac{5}{5} + \frac{7}{5 x y}$

Step 6

To write $\frac{7}{5 x y}$ as a fraction with a common denominator, multiply by $\frac{2 y^{2} x}{2 y^{2} x}$ .

$\frac{2 y^{3} - 3 x}{2 y^{3} x^{2}} \cdot \frac{5}{5} + \frac{7}{5 x y} \cdot \frac{2 y^{2} x}{2 y^{2} x}$

Step 7

Write each expression with a common denominator of $10 y^{3} x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 7.1

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

$\frac{(2 y^{3} - 3 x) \cdot 5}{2 y^{3} x^{2} \cdot 5} + \frac{7}{5 x y} \cdot \frac{2 y^{2} x}{2 y^{2} x}$

Step 7.2

Multiply $5$ by $2$ .

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7}{5 x y} \cdot \frac{2 y^{2} x}{2 y^{2} x}$

Step 7.3

Multiply $\frac{7}{5 x y}$ by $\frac{2 y^{2} x}{2 y^{2} x}$ .

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{5 x y (2 y^{2} x)}$

Step 7.4

Multiply $2$ by $5$ .

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{10 x y (y^{2} x)}$

Step 7.5

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

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{10 (x^{1} x) y \cdot y^{2}}$

Step 7.6

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

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{10 (x^{1} x^{1}) y \cdot y^{2}}$

Step 7.7

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

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{10 x^{1 + 1} y \cdot y^{2}}$

Step 7.8

Add $1$ and $1$ .

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{10 x^{2} y \cdot y^{2}}$

Step 7.9

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

Tap for more steps...

Step 7.9.1

Move $y^{2}$ .

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{10 x^{2} (y^{2} y)}$

Step 7.9.2

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

Tap for more steps...

Step 7.9.2.1

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

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{10 x^{2} (y^{2} y^{1})}$

Step 7.9.2.2

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

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{10 x^{2} y^{2 + 1}}$

Step 7.9.3

Add $2$ and $1$ .

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{10 x^{2} y^{3}}$

Step 7.10

Reorder the factors of $10 x^{2} y^{3}$ .

$\frac{(2 y^{3} - 3 x) \cdot 5}{10 y^{3} x^{2}} + \frac{7 (2 y^{2} x)}{10 y^{3} x^{2}}$

Step 8

Combine the numerators over the common denominator.

$\frac{(2 y^{3} - 3 x) \cdot 5 + 7 (2 y^{2} x)}{10 y^{3} x^{2}}$

Step 9

Simplify the numerator.

Tap for more steps...

Step 9.1

Apply the distributive property.

$\frac{2 y^{3} \cdot 5 - 3 x \cdot 5 + 7 \cdot 2 y^{2} x}{10 y^{3} x^{2}}$

Step 9.2

Multiply $5$ by $2$ .

$\frac{10 y^{3} - 3 x \cdot 5 + 7 \cdot 2 y^{2} x}{10 y^{3} x^{2}}$

Step 9.3

Multiply $5$ by $- 3$ .

$\frac{10 y^{3} - 15 x + 7 \cdot 2 y^{2} x}{10 y^{3} x^{2}}$

Step 9.4

Multiply $7$ by $2$ .

$\frac{10 y^{3} - 15 x + 14 y^{2} x}{10 y^{3} x^{2}}$