Basic Math Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 3.5

Add $1$ and $1$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

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

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

Step 6

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

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Step 6.1

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

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

Step 6.2

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

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

Step 6.3

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

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

Step 6.4

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

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

Step 6.5

Add $1$ and $1$ .

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

Step 6.6

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

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Multiply $3$ by $2$ .

$\frac{- 5 + 7 x + 6 y}{2 x^{2} y^{2}}$

Step 9

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- 1 (5) + 7 x + 6 y}{2 x^{2} y^{2}}$

Step 10

Factor $- 1$ out of $7 x$ .

$\frac{- 1 (5) - (- 7 x) + 6 y}{2 x^{2} y^{2}}$

Step 11

Factor $- 1$ out of $- 1 (5) - (- 7 x)$ .

$\frac{- 1 (5 - 7 x) + 6 y}{2 x^{2} y^{2}}$

Step 12

Factor $- 1$ out of $6 y$ .

$\frac{- 1 (5 - 7 x) - (- 6 y)}{2 x^{2} y^{2}}$

Step 13

Factor $- 1$ out of $- 1 (5 - 7 x) - (- 6 y)$ .

$\frac{- 1 (5 - 7 x - 6 y)}{2 x^{2} y^{2}}$

Step 14

Move the negative in front of the fraction.

$- \frac{5 - 7 x - 6 y}{2 x^{2} y^{2}}$