Question 36749
{{{ (x-2)/(x-3) = (x-1)/(x+1) }}}
Cross multiply
{{{ (x-2)(x+1)=(x-3)(x-1) }}}
FOIL both sides
{{{ x^2 -1x -2 = x^2 -4x +3 }}}
the x^2 cancel each other out since they are of the same coefficient and sign
{{{ -1x -2 = -4x +3 }}}
Add 4x and 2 to both sides
{{{ 3x = 5 }}}
divide by 3
{{{ x= 5/3 }}}
Plug this into each of the denominators.
{{{ (5/3) - 3 }}} and {{{ (5/3) + 1 }}}
{{{ (5/3) - (9/3) }}} and {{{ (5/3) + (3/3) }}}
{{{ (-4/3) }}} and {{{ (8/3) }}}
Neither of these comes out to be zero, so both are solutions to the rational equation