Algebra Examples

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

Step 1

Factor each term.

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Step 1.1

Move the negative in front of the fraction.

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

Step 1.2

Reduce the expression by cancelling the common factors.

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Step 1.2.1

Reduce the expression $\frac{x - 5}{x - 5}$ by cancelling the common factors.

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Step 1.2.1.1

Cancel the common factor.

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

Step 1.2.1.2

Rewrite the expression.

$- \frac{3}{x + 1} = \frac{1}{1}$

Step 1.2.2

Rewrite the expression.

$- \frac{3}{x + 1} = 1$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x + 1, 1$

Step 2.2

Remove parentheses.

$x + 1, 1$

Step 2.3

The LCM of one and any expression is the expression.

$x + 1$

Step 3

Multiply each term in $- \frac{3}{x + 1} = 1$ by $x + 1$ to eliminate the fractions.

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Step 3.1

Multiply each term in $- \frac{3}{x + 1} = 1$ by $x + 1$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x + 1$ .

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Step 3.2.1.1

Move the leading negative in $- \frac{3}{x + 1}$ into the numerator.

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

Step 3.2.1.2

Cancel the common factor.

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

Step 3.2.1.3

Rewrite the expression.

$- 3 = 1 (x + 1)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $x + 1$ by $1$ .

$- 3 = x + 1$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $x + 1 = - 3$ .

$x + 1 = - 3$

Step 4.2

Move all terms not containing $x$ to the right side of the equation.

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Step 4.2.1

Subtract $1$ from both sides of the equation.

$x = - 3 - 1$

Step 4.2.2

Subtract $1$ from $- 3$ .

$x = - 4$