Algebra Examples

$\frac{4 x + 1}{7 x^{2}} - \frac{1 - 3 x}{7 x^{2}}$

Step 1

Combine the numerators over the common denominator.

$\frac{4 x + 1 - (1 - 3 x)}{7 x^{2}}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{4 x + 1 - 1 \cdot 1 - (- 3 x)}{7 x^{2}}$

Step 2.2

Multiply $- 1$ by $1$ .

$\frac{4 x + 1 - 1 - (- 3 x)}{7 x^{2}}$

Step 2.3

Multiply $- 3$ by $- 1$ .

$\frac{4 x + 1 - 1 + 3 x}{7 x^{2}}$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $4 x + 1 - 1 + 3 x$ .

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Step 3.1.1

Subtract $1$ from $1$ .

$\frac{4 x + 0 + 3 x}{7 x^{2}}$

Step 3.1.2

Add $4 x$ and $0$ .

$\frac{4 x + 3 x}{7 x^{2}}$

Step 3.2

Add $4 x$ and $3 x$ .

$\frac{7 x}{7 x^{2}}$

Step 3.3

Cancel the common factor of $7$ .

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Step 3.3.1

Cancel the common factor.

$\frac{7 x}{7 x^{2}}$

Step 3.3.2

Rewrite the expression.

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

Step 3.4

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

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Step 3.4.1

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

$\frac{x^{1}}{x^{2}}$

Step 3.4.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1}{x^{2}}$

Step 3.4.3

Cancel the common factors.

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Step 3.4.3.1

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

$\frac{x \cdot 1}{x \cdot x}$

Step 3.4.3.2

Cancel the common factor.

$\frac{x \cdot 1}{x \cdot x}$

Step 3.4.3.3

Rewrite the expression.

$\frac{1}{x}$