Solve: 2/(x-1) - 1/2 = 4/(x^2-1)

Question

Solve: 

2/(x-1) - 1/2 = 4/(x^2-1)

Answer 1

The least common multiple for the denominator is
LCM=2(x-1)(x+1). Multiply each term by the LCM to get...

4(x-1)-(x-1)(x+1)=8
           4x-4-x²+1=8......distribute and expand terms
            -x²+4x+5=8......combine terms, rewrite equation

             -x²+4x-3=0......subtract 8 both sides

            (x-1)(x-3)=0......factor

x-1=0   -or-    x-3=0.......let each term equal to zero, solve for "x"

   x=1               x=3

 

Now from the problem statement equation, we can conclude that 

the value "x=1" cannot be a solution because the first term would 

then have zero in the denominator, division by zero is undefined.

 

So "x=3" is the single solution To the equation.  Substitute back into the original equation and check for truth...

2/(3-2)-1/2=4/(3²-1)

 (2/2)-(1/2)=4/(9-1)

         1-1/2=4/8

            1/2=1/2..........√check, solution is correct.  Always check 

                                   your solution, work