# How do you simplify  [6 / (X-1)] = [4 / (X+1)]?

May 11, 2018

$x$ is $- 1$.

#### Explanation:

1. Step 1: Cross-Multiply
This means we multiply each numerator by the opposite denominator and this helps to clear the fraction.
$6 \left(x + 1\right) = 4 \left(x - 1\right)$

2. Step 2: Distribute
We need to distribute or multiply out both sides of the equation to simplify them.
$6 x + 6 = 4 x - 4$

3. Step 3: Isolate the Variable
Because we want to solve for $x$, we must isolate it on one side of the equation.
$6 x - 4 x = - 4 - 6$

4. Step 4: Simplify
We can now complete the addition and subtraction to simplify the equation.
$2 x = - 10$

5. Step 5: Divide
Because $x$ is multiplied by $2$, we must divide both sides by $2$, so that $x$ is alone. This way, we can find the value of $x$, instead of multiples of it.
$x = - 5$

6. Step 6: Check
We can check that our answer is correct by plugging it back in to the original equation.
$\frac{6}{- 5 - 1} = \frac{4}{- 5 + 1}$
$\frac{6}{-} 6 = \frac{4}{-} 4$
$- 1 = - 1$