Question 159351
{{{1/(r^2-1)=2/(r^2+r-2)}}} Start with the given equation.



{{{1/((r+1)(r-1))=2/(r^2+r-2)}}} Factor {{{r^2-1}}} to get {{{(r+1)(r-1)}}}



{{{1/((r+1)(r-1))=2/((r+2)(r-1))}}} Factor {{{r^2+r-2}}} to get {{{(r+2)(r-1)}}}



{{{1(r+2)=2(r+1)}}} Multiply both sides by the LCD {{{(r+1)(r-1)(r+2)}}} to clear the fractions.



{{{r+2=2r+2}}} Distribute.



{{{r=2r+2-2}}} Subtract {{{2}}} from both sides.



{{{r-2r=2-2}}} Subtract {{{2r}}} from both sides.



{{{-r=2-2}}} Combine like terms on the left side.



{{{-r=0}}} Combine like terms on the right side.



{{{r=(0)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{r}}}.



{{{r=0}}} Reduce.



----------------------------------------------------------------------


Answer:


So the answer is {{{r=0}}}