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

Question :

frac6x - 1 + frac5x + 1 = frac6x - 1

x \in \emptyset

Alternative Form

No solution

Evaluate

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

Find the domain

More Steps

\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

More Steps

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

Simplify the equation

More Steps

11 x + 1 = 6 x + 6

Move the expression to the left side

11 x + 1 - 6 x = 6

Move the expression to the right side

11 x - 6 x = 6 - 1

Add and subtract

More Steps

5 x = 6 - 1

Add and subtract

5 x = 5

Divide both sides

\frac{5 x}{5} = \frac{5}{5}

Divide the numbers

x = \frac{5}{5}

Divide the numbers

More Steps

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

Show Solution