Question 321516
{{{4-x/(x-2)=-2/(x-2)}}} Start with the given equation.



{{{4(x-2)-x=-2}}} Multiply EVERY term by the LCD {{{x-2}}} to clear out the fractions.



{{{4x-8-x=-2}}} Distribute.



{{{3x-8=-2}}} Combine like terms on the left side.



{{{3x=-2+8}}} Add {{{8}}} to both sides.



{{{3x=6}}} Combine like terms on the right side.



{{{x=(6)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=2}}} Reduce.



So the only possible solution is {{{x=2}}}. However, if you plug it into the original equation, you get a division by zero, which is not allowed. So {{{x<>2}}} and that means that there are NO solutions.