Algebra Examples

$\frac{9 x}{x + 1} = 4 - \frac{9}{x + 1}$

Step 1

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

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Step 1.1

Subtract $4$ from both sides of the equation.

$\frac{9 x}{x + 1} - 4 = - \frac{9}{x + 1}$

Step 1.2

Add $\frac{9}{x + 1}$ to both sides of the equation.

$\frac{9 x}{x + 1} - 4 + \frac{9}{x + 1} = 0$

Step 2

Simplify $\frac{9 x}{x + 1} - 4 + \frac{9}{x + 1}$ .

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Step 2.1

Find the common denominator.

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Step 2.1.1

Write $- 4$ as a fraction with denominator $1$ .

$\frac{9 x}{x + 1} + \frac{- 4}{1} + \frac{9}{x + 1} = 0$

Step 2.1.2

Multiply $\frac{- 4}{1}$ by $\frac{x + 1}{x + 1}$ .

$\frac{9 x}{x + 1} + \frac{- 4}{1} \cdot \frac{x + 1}{x + 1} + \frac{9}{x + 1} = 0$

Step 2.1.3

Multiply $\frac{- 4}{1}$ by $\frac{x + 1}{x + 1}$ .

$\frac{9 x}{x + 1} + \frac{- 4 (x + 1)}{x + 1} + \frac{9}{x + 1} = 0$

Step 2.2

Combine the numerators over the common denominator.

$\frac{9 x - 4 (x + 1) + 9}{x + 1} = 0$

Step 2.3

Simplify each term.

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Step 2.3.1

Apply the distributive property.

$\frac{9 x - 4 x - 4 \cdot 1 + 9}{x + 1} = 0$

Step 2.3.2

Multiply $- 4$ by $1$ .

$\frac{9 x - 4 x - 4 + 9}{x + 1} = 0$

Step 2.4

Subtract $4 x$ from $9 x$ .

$\frac{5 x - 4 + 9}{x + 1} = 0$

Step 2.5

Add $- 4$ and $9$ .

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

Step 2.6

Factor $5$ out of $5 x + 5$ .

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Step 2.6.1

Factor $5$ out of $5 x$ .

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

Step 2.6.2

Factor $5$ out of $5$ .

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

Step 2.6.3

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

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

Step 2.7

Cancel the common factor of $x + 1$ .

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Step 2.7.1

Cancel the common factor.

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

Step 2.7.2

Divide $5$ by $1$ .

$5 = 0$

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.