Question

subtract, simplfy by removing a factor of 1 when possible.

19dc/d^2-c^2 - d-c/d+c

Answer 1

You must mean ....

19cd/(d^2 - c^2) - (d-c)/(d+c)
then ...

= 19cd/((d+c)(d-c) - (d-c)/(d+c)
LCD is (d+c)(d-c)

= ( 19cd - (d-c)(d+c) )/((d+c)(d-c) )
= (c^2 + 19cd - d^2)/(d^2 - c^2)

not much of a simplication.
Confirm if my assumption of the question was correct.