Question 72429
You must have common denominators.
{{{ (5)/(x+y) }}} + {{{ (5)/(x^2-y^2) }}}
Factor the second denominator
{{{ (5)/(x+y) }}} + {{{ (5)/((x-y)(x+y)) }}}
Multiply the first fraction by (x-y)/(x-y)
{{{ ((5)(x-y))/((x+y)(x-y)) }}} + {{{ (5)/((x-y)(x+y)) }}}
Distribute the 5 in the first numerator
{{{ ((5x-5y))/((x+y)(x-y)) }}} + {{{ (5)/((x-y)(x+y)) }}}
Combine the two fractions by adding the numerators
{{{ (5x-5y+5)/((x+y)(x-y)) }}}
You can factor out a 5 from the numerator if your instructor wants you so go that far
{{{ (5(x-y+1))/((x+y)(x-y)) }}}