Question 705278
Given:: {{{2/(X-1) = 4/(X-3) - 1/(X+1)}}}
I would start by multiplying everything by each of the denominators
{{{2/(X-1)*(X-1)*(X-3)*(X+1) = 4/(X-3)*(X-1)*(X-3)*(X+1) - 1/(X+1)*(X-1)*(X-3)*(X+1)}}}
Then the denominators will cancel out
{{{2/cross((X-1))*cross((X-1))*(X-3)*(X+1) = 4/cross((X-3))*(X-1)*cross((X-3))*(X+1) - 1/cross((X+1))*(X-1)*(X-3)*cross((X+1))}}}
Rewrite the equation.
{{{2*(X-3)*(X+1) = 4*(X-1)*(X+1) - 1*(X-1)*(X-3)}}}
Start to multiply through
{{{(2X - 6)*(X+1) = (4X-4)*(X+1) + (-X+1)*(X-3)}}}
Multiply through
{{{2X^2 + 2X - 6X - 6 = 4X^2 + 4X - 4X - 4 - X^2 + 3X + X - 3}}}
Combine like terms
{{{2X^2 - 4X - 6 = 3X^2 + 4X - 7}}}
Subtract 2X^2 from both sides
{{{-4X - 6 = X^2 + 4X - 7}}}
Add 4X to both sides
{{{-6 = X^2 + 8X - 7}}}
Add 6 to both sides
{{{0 = X^2 + 8X - 1}}}
Now use the quadratic equation.
*[invoke quadratic "X",1,8,-1]
So X = 0.1231 & -8.1231