Question

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

Answer 1

`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(x+1)=4(x-1)`

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

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

4. Step 4: Simplify
   We can now complete the addition and subtraction to simplify the equation.
   `2x=-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.
   `6/(-5-1)=4/(-5+1)`
   `6/-6=4/-4`
   `-1=-1`
   The answer is proven.