Solve by Factoring 1/(x+1)+4=9/(x+1)

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

Step 1

Subtract $\frac{9}{x + 1}$ from both sides of the equation.

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

Step 2

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

Combine the numerators over the common denominator.

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

Subtract $9$ from $1$ .

$4 + \frac{- 8}{x + 1} = 0$

Move the negative in front of the fraction.

$4 - \frac{8}{x + 1} = 0$

To write $4$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$\frac{4 (x + 1)}{x + 1} - \frac{8}{x + 1} = 0$

Combine the numerators over the common denominator.

$\frac{4 (x + 1) - 8}{x + 1} = 0$

Simplify the numerator.

Factor $4$ out of $4 (x + 1) - 8$ .

Factor $4$ out of $- 8$ .

$\frac{4 (x + 1) + 4 \cdot - 2}{x + 1} = 0$

Factor $4$ out of $4 (x + 1) + 4 \cdot - 2$ .

$\frac{4 (x + 1 - 2)}{x + 1} = 0$

Subtract $2$ from $1$ .

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

Step 3

Set the numerator equal to zero.

$4 (x - 1) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $4 (x - 1) = 0$ by $4$ and simplify.

Divide each term in $4 (x - 1) = 0$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x - 1$ by $1$ .

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

Simplify the right side.

Divide $0$ by $4$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$