Solve \frac{6}{x-1}+\frac{5}{x+1}=\frac{6}{x-1}

Evaluate

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

Find the domain

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\frac{6}{x - 1} + \frac{5}{x + 1} = \frac{6}{x - 1}, x \in (- \infty, - 1) \cup (- 1, 1) \cup (1, + \infty)

Multiply both sides of the equation by LCD

(\frac{6}{x - 1} + \frac{5}{x + 1}) (x - 1) (x + 1) = \frac{6}{x - 1} \times (x - 1) (x + 1)

Simplify the equation

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11 x + 1 = \frac{6}{x - 1} \times (x - 1) (x + 1)

Simplify the equation

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11 x + 1 = 6 x + 6

Move the variable to the left side

11 x + 1 - 6 x = 6

Subtract the terms

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5 x + 1 = 6

Move the constant to the right side

5 x = 6 - 1

Subtract the terms

5 x = 5

Multiply both sides of the equation by \frac{1}{5}

5 x \times \frac{1}{5} = 5 \times \frac{1}{5}

Reduce the numbers

5 x \times \frac{1}{5} = 1

Cancel out the greatest common factor 5

x = 1

Check if the solution is in the defined range

x = 1, x \in (- \infty, - 1) \cup (- 1, 1) \cup (1, + \infty)

Solution

x \in \emptyset

Alternative Form

No solution