Question 657012
{{{1/x - 1/(x+1) = 3}}}
{{{((x+1)/(x+1)) * (1/(x+1)) - (x/x)*(1/(x+1)) = 3}}}
{{{(x+1)/(x^2 + x) - x/(x^2 + x) = 3}}}
{{{(x + 1 - x) / (x^2 + x) = 3}}}
{{{1/(x^2 + x) = 3}}}
{{{(x^2+x)*(1/(x^2+x)) = 3*(x^2+x)}}}
{{{1 = 3*x^2 + 3*x}}}
{{{3*x^2 + 3*x - 1 = 3}}}
We can solve for x using the quadratic equation {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} with x=3, b=3, and c=-1
{{{x = (-3 +- sqrt( 3^2-4*3*(-1) ))/(2*3) }}}
{{{x = (-3 +- sqrt( 9+12 ))/6 }}}
{{{x = (-3 +- sqrt( 21 ))/6 }}}
So x = -1.264 or x = 0.264 (rounded to three decimal places).
{{{1/(-1.264) - 1/(-1.264+1) = -0.179 - -3.179 = 3}}}
{{{1/0.264 - 1/(0.264+1) = 3.179 - 0.791 = 3}}}