In the expression (3/k-9)+(1/9-k) what are the possible lcd/s

The possible LCD/s  would be  -1(k-9) or -k +9

or 18k -k²-81

Step-by-step explanation:

(3/k-9)+(1/9-k)

If we observe carefully we find that the denominators are the same only with the change of signs. This can be solved in the following way

Rearranging the above expression would give

(3/k-9)+(1/-k+9)

or taking (-1) common from the second denominator

(3/k-9)+(1/-1(k-9) )

So the LCD would be  -1(k-9) or -k +9

(-1(3)/-1(k-9)+(1/-1(k-9) )

= (-3/-k+9)+(1/-k+9 )

Another way used can be to multiply both denominators

k-9

9-k

9k -81

-k²+9k

18k -k²-81

And multiply each numerator with the other fraction's denominator to solve the question.