Algebra Examples

$\frac{1}{x - 1} + 5 = \frac{11}{x - 1}$

Step 1

Subtract $\frac{11}{x - 1}$ from both sides of the equation.

$\frac{1}{x - 1} + 5 - \frac{11}{x - 1} = 0$

Step 2

Simplify $\frac{1}{x - 1} + 5 - \frac{11}{x - 1}$ .

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Step 2.1

Combine the numerators over the common denominator.

$5 + \frac{1 - 11}{x - 1} = 0$

Step 2.2

Subtract $11$ from $1$ .

$5 + \frac{- 10}{x - 1} = 0$

Step 2.3

Move the negative in front of the fraction.

$5 - \frac{10}{x - 1} = 0$

Step 2.4

To write $5$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$\frac{5 (x - 1)}{x - 1} - \frac{10}{x - 1} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{5 (x - 1) - 10}{x - 1} = 0$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Factor $5$ out of $5 (x - 1) - 10$ .

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Step 2.6.1.1

Factor $5$ out of $- 10$ .

$\frac{5 (x - 1) + 5 \cdot - 2}{x - 1} = 0$

Step 2.6.1.2

Factor $5$ out of $5 (x - 1) + 5 \cdot - 2$ .

$\frac{5 (x - 1 - 2)}{x - 1} = 0$

Step 2.6.2

Subtract $2$ from $- 1$ .

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

Step 3

Set the denominator in $\frac{5 (x - 3)}{x - 1}$ equal to $0$ to find where the expression is undefined.

$x - 1 = 0$

Step 4

Add $1$ to both sides of the equation.

$x = 1$

Step 5