Pre-Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Combine the opposite terms in $3 x - 1 + 7 x + 1$ .

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Step 2.1

Add $- 1$ and $1$ .

$\frac{3 x + 7 x + 0}{5 x^{2} y}$

Step 2.2

Add $3 x + 7 x$ and $0$ .

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

Step 3

Add $3 x$ and $7 x$ .

$\frac{10 x}{5 x^{2} y}$

Step 4

Cancel the common factor of $10$ and $5$ .

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Step 4.1

Factor $5$ out of $10 x$ .

$\frac{5 (2 x)}{5 x^{2} y}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{5 (2 x)}{5 (x^{2} y)}$

Step 4.2.2

Cancel the common factor.

$\frac{5 (2 x)}{5 (x^{2} y)}$

Step 4.2.3

Rewrite the expression.

$\frac{2 x}{x^{2} y}$

Step 5

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

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Step 5.1

Factor $x$ out of $2 x$ .

$\frac{x \cdot 2}{x^{2} y}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{x \cdot 2}{x (x y)}$

Step 5.2.2

Cancel the common factor.

$\frac{x \cdot 2}{x (x y)}$

Step 5.2.3

Rewrite the expression.

$\frac{2}{x y}$