Algebra Examples

$\frac{- 3}{x + 3} = \frac{x}{x + 3} - \frac{x}{5}$

Step 1

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

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Step 1.1

Subtract $\frac{x}{x + 3}$ from both sides of the equation.

$\frac{- 3}{x + 3} - \frac{x}{x + 3} = - \frac{x}{5}$

Step 1.2

Add $\frac{x}{5}$ to both sides of the equation.

$\frac{- 3}{x + 3} - \frac{x}{x + 3} + \frac{x}{5} = 0$

Step 2

Simplify $\frac{- 3}{x + 3} - \frac{x}{x + 3} + \frac{x}{5}$ .

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Step 2.1

Move the negative in front of the fraction.

$- \frac{3}{x + 3} - \frac{x}{x + 3} + \frac{x}{5} = 0$

Step 2.2

Combine the numerators over the common denominator.

$\frac{- 3 - x}{x + 3} + \frac{x}{5} = 0$

Step 2.3

Cancel the common factor of $- 3 - x$ and $x + 3$ .

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Step 2.3.1

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- 1 (3) - x}{x + 3} + \frac{x}{5} = 0$

Step 2.3.2

Factor $- 1$ out of $- x$ .

$\frac{- 1 (3) - (x)}{x + 3} + \frac{x}{5} = 0$

Step 2.3.3

Factor $- 1$ out of $- 1 (3) - (x)$ .

$\frac{- 1 (3 + x)}{x + 3} + \frac{x}{5} = 0$

Step 2.3.4

Reorder terms.

$\frac{- 1 (x + 3)}{x + 3} + \frac{x}{5} = 0$

Step 2.3.5

Cancel the common factor.

$\frac{- 1 (x + 3)}{x + 3} + \frac{x}{5} = 0$

Step 2.3.6

Divide $- 1$ by $1$ .

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

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.