Question 119617


{{{(x^2+6x-16)/(x-2)=x+8}}} Start with the given equation. Note: since {{{x<>2}}} since that will make the denominator equal to zero


{{{((x+8)(x-2))/(x-2)=x+8}}}   Factor {{{x^2+6x-16}}} to get {{{(x+8)(x-2)}}} 



{{{(x+8)(x-2)/(x-2)=x+8}}} Combine the fractions



{{{(x+8)cross((x-2))/cross((x-2))=x+8}}} Cancel like terms



{{{x+8=x+8}}} Simplify




{{{x=x+8-8}}}Subtract 8 from both sides



{{{x-x=8-8}}} Subtract x from both sides



{{{0x=8-8}}} Combine like terms on the left side



{{{0x=0}}} Combine like terms on the right side



{{{0=0}}} Simplify


Since this equation is always true for any x value, this means  {{{(x^2+6x-16)/(x-2)=x+8}}} is an identity and x can equal any number except 2.