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

1 Answer
May 11, 2018

Answer:

#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.