Algebra Examples

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

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $5$ from both sides of the equation.

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

Step 1.2

Add $\frac{7}{x + 1}$ to both sides of the equation.

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

Step 2

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

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Step 2.1

Find the common denominator.

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Step 2.1.1

Write $- 5$ as a fraction with denominator $1$ .

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

Step 2.1.2

Multiply $\frac{- 5}{1}$ by $\frac{x + 1}{x + 1}$ .

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

Step 2.1.3

Multiply $\frac{- 5}{1}$ by $\frac{x + 1}{x + 1}$ .

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Simplify each term.

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Step 2.3.1

Apply the distributive property.

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

Step 2.3.2

Multiply $- 5$ by $1$ .

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

Step 2.4

Subtract $5 x$ from $7 x$ .

$\frac{2 x - 5 + 7}{x + 1} = 0$

Step 2.5

Add $- 5$ and $7$ .

$\frac{2 x + 2}{x + 1} = 0$

Step 2.6

Factor $2$ out of $2 x + 2$ .

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Step 2.6.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 2}{x + 1} = 0$

Step 2.6.2

Factor $2$ out of $2$ .

$\frac{2 (x) + 2 (1)}{x + 1} = 0$

Step 2.6.3

Factor $2$ out of $2 (x) + 2 (1)$ .

$\frac{2 (x + 1)}{x + 1} = 0$

Step 2.7

Cancel the common factor of $x + 1$ .

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Step 2.7.1

Cancel the common factor.

$\frac{2 (x + 1)}{x + 1} = 0$

Step 2.7.2

Divide $2$ by $1$ .

$2 = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.