Algebra Examples

$\frac{x - 5}{4 x} + 1 = \frac{x + 7}{x}$

Step 1

Subtract $\frac{x + 7}{x}$ from both sides of the equation.

$\frac{x - 5}{4 x} + 1 - \frac{x + 7}{x} = 0$

Step 2

Simplify $\frac{x - 5}{4 x} + 1 - \frac{x + 7}{x}$ .

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Step 2.1

Write $1$ as a fraction with a common denominator.

$\frac{x - 5}{4 x} + \frac{4 x}{4 x} - \frac{x + 7}{x} = 0$

Step 2.2

Combine the numerators over the common denominator.

$\frac{x - 5 + 4 x}{4 x} - \frac{x + 7}{x} = 0$

Step 2.3

Add $x$ and $4 x$ .

$\frac{5 x - 5}{4 x} - \frac{x + 7}{x} = 0$

Step 2.4

Factor $5$ out of $5 x - 5$ .

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Step 2.4.1

Factor $5$ out of $5 x$ .

$\frac{5 (x) - 5}{4 x} - \frac{x + 7}{x} = 0$

Step 2.4.2

Factor $5$ out of $- 5$ .

$\frac{5 (x) + 5 (- 1)}{4 x} - \frac{x + 7}{x} = 0$

Step 2.4.3

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

$\frac{5 (x - 1)}{4 x} - \frac{x + 7}{x} = 0$

Step 2.5

To write $- \frac{x + 7}{x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 (x - 1)}{4 x} - \frac{x + 7}{x} \cdot \frac{4}{4} = 0$

Step 2.6

Write each expression with a common denominator of $4 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.6.1

Multiply $\frac{x + 7}{x}$ by $\frac{4}{4}$ .

$\frac{5 (x - 1)}{4 x} - \frac{(x + 7) \cdot 4}{x \cdot 4} = 0$

Step 2.6.2

Reorder the factors of $x \cdot 4$ .

$\frac{5 (x - 1)}{4 x} - \frac{(x + 7) \cdot 4}{4 x} = 0$

Step 2.7

Combine the numerators over the common denominator.

$\frac{5 (x - 1) - (x + 7) \cdot 4}{4 x} = 0$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Apply the distributive property.

$\frac{5 x + 5 \cdot - 1 - (x + 7) \cdot 4}{4 x} = 0$

Step 2.8.2

Multiply $5$ by $- 1$ .

$\frac{5 x - 5 - (x + 7) \cdot 4}{4 x} = 0$

Step 2.8.3

Apply the distributive property.

$\frac{5 x - 5 + (- x - 1 \cdot 7) \cdot 4}{4 x} = 0$

Step 2.8.4

Multiply $- 1$ by $7$ .

$\frac{5 x - 5 + (- x - 7) \cdot 4}{4 x} = 0$

Step 2.8.5

Apply the distributive property.

$\frac{5 x - 5 - x \cdot 4 - 7 \cdot 4}{4 x} = 0$

Step 2.8.6

Multiply $4$ by $- 1$ .

$\frac{5 x - 5 - 4 x - 7 \cdot 4}{4 x} = 0$

Step 2.8.7

Multiply $- 7$ by $4$ .

$\frac{5 x - 5 - 4 x - 28}{4 x} = 0$

Step 2.8.8

Subtract $4 x$ from $5 x$ .

$\frac{x - 5 - 28}{4 x} = 0$

Step 2.8.9

Subtract $28$ from $- 5$ .

$\frac{x - 33}{4 x} = 0$

Step 3

Set the denominator in $\frac{x - 33}{4 x}$ equal to $0$ to find where the expression is undefined.

$4 x = 0$

Step 4

Divide each term in $4 x = 0$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $4$ .

$x = 0$

Step 5