To subtract or add and simplify these two fractions they must be over a common denominator. Multiply the fraction on the right by the appropriate form of #1# which is (#(-1)/-1#):
#(k^2 - 26)/(k - 5) - ((-1)/-1 xx 1/(5 - k)) =>#
#(k^2 - 26)/(k - 5) - (-1/(-1(5 - k))) =>#
#(k^2 - 26)/(k - 5) - (-1/((-1 xx 5) - (-1 xx k))) =>#
#(k^2 - 26)/(k - 5) - (-1/(-5 - (-1k))) =>#
#(k^2 - 26)/(k - 5) - (-1/(-5 + 1k))) =>#
#(k^2 - 26)/(k - 5) - (-1/(-5 + k))) =>#
#(k^2 - 26)/(k - 5) - (-1/(k - 5)) =>#
#(k^2 - 26)/(k - 5) + 1/(k - 5)#
We can now add the numerator over the common denominator:
#(k^2 - 26 + 1)/(k - 5)#
#(k^2 - 25)/(k - 5)#
The numerator is a special for of the quadratic:
#a^2 - b^2 = (a + b)(a - b)#
We can factor the remaining fraction as:
#((k + 5)(k - 5))/(k - 5)#
We can now cancel common terms in the numerator and denominator:
#((k + 5)color(red)(cancel(color(black)((k - 5)))))/color(red)(cancel(color(black)(k - 5))) =>#
#k + 5# Where, from the original expression #k != 5#
