Question 183375
{{{(x-2)/(x^2-25) - (x-2)/(25-x^2)}}} Start with the given expression



{{{(x-2)/(x^2-25) - (x-2)/(-x^2+25)}}} Rearrange {{{25-x^2}}} to get {{{-x^2+25}}}



{{{(x-2)/(x^2-25) - (x-2)/(-(x^2-25))}}} Factor {{{-x^2+25}}} to get {{{-(x^2-25)}}}



{{{(x-2)/(x^2-25) + (x-2)/(x^2-25)}}} Reduce



Since the denominators are now equal, we can add the fractions:



{{{(x-2+ (x-2))/(x^2-25)}}} Combine the fractions.



{{{(2x-4)/(x^2-25)}}} Combine like terms.



So {{{(x-2)/(x^2-25) - (x-2)/(25-x^2)}}} simplifies to {{{(2x-4)/(x^2-25)}}}