Solve by Factoring 5-4/(x+1)=6

$5 - \frac{4}{x + 1} = 6$

Step 1

Subtract $6$ from both sides of the equation.

$5 - \frac{4}{x + 1} - 6 = 0$

Step 2

Simplify $5 - \frac{4}{x + 1} - 6$ .

Find the common denominator.

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

$\frac{5}{1} - \frac{4}{x + 1} - 6 = 0$

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

$\frac{5}{1} \cdot \frac{x + 1}{x + 1} - \frac{4}{x + 1} - 6 = 0$

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

$\frac{5 (x + 1)}{x + 1} - \frac{4}{x + 1} - 6 = 0$

Write $- 6$ as a fraction with denominator $1$ .

$\frac{5 (x + 1)}{x + 1} - \frac{4}{x + 1} + \frac{- 6}{1} = 0$

Multiply $\frac{- 6}{1}$ by $\frac{x + 1}{x + 1}$ .

$\frac{5 (x + 1)}{x + 1} - \frac{4}{x + 1} + \frac{- 6}{1} \cdot \frac{x + 1}{x + 1} = 0$

Multiply $\frac{- 6}{1}$ by $\frac{x + 1}{x + 1}$ .

$\frac{5 (x + 1)}{x + 1} - \frac{4}{x + 1} + \frac{- 6 (x + 1)}{x + 1} = 0$

Combine the numerators over the common denominator.

$\frac{5 (x + 1) - 4 - 6 (x + 1)}{x + 1} = 0$

Simplify each term.

Apply the distributive property.

$\frac{5 x + 5 \cdot 1 - 4 - 6 (x + 1)}{x + 1} = 0$

Multiply $5$ by $1$ .

$\frac{5 x + 5 - 4 - 6 (x + 1)}{x + 1} = 0$

Apply the distributive property.

$\frac{5 x + 5 - 4 - 6 x - 6 \cdot 1}{x + 1} = 0$

Multiply $- 6$ by $1$ .

$\frac{5 x + 5 - 4 - 6 x - 6}{x + 1} = 0$

Subtract $6 x$ from $5 x$ .

$\frac{- x + 5 - 4 - 6}{x + 1} = 0$

Subtract $4$ from $5$ .

$\frac{- x + 1 - 6}{x + 1} = 0$

Subtract $6$ from $1$ .

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

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

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

Rewrite $- 5$ as $- 1 (5)$ .

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

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

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

Rewrite $- (x + 5)$ as $- 1 (x + 5)$ .

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

Move the negative in front of the fraction.

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

Step 3

Set the numerator equal to zero.

$x + 5 = 0$

Step 4

Subtract $5$ from both sides of the equation.

$x = - 5$

Solve by Factoring 5-4/(x+1)=6

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