Rational expression (d / d - b) - (d / b - d)?

d/(d - b) - d/(b - d)
= d/(d - b) - d/[-(-b + d)]
= d/(d - b) - (-d)/(d - b)]
= d/(d - b) + d/(d - b)
= 2d/(d - b)

or

d/(d - b) - d/(b - d)
= d/[-(-d + b) - d/(b - d)
= -d/(b - d) - d/(b - d)
= -2d/(b - d)

Actually, both are correct.

=d/(d-b) +d/(d-b)=2d/(d-b)
God bless you.They are tha same.

(d / d - b) - (d / b - d)

1 - b - d / b + d

Cannot be simplified more.

Unless of course you meant:
d / (d - b) - d / (b - d)

d / (d - b) + d / (d - b)

2d / (d - b)

to make everythiing run together smoothly, you must find a common denominator.
multiply fraction 1 by the second denominator:
(b-d)/(b-d) * (d/d-b) = (-d^2 + db) / (-d^2 - b^2 + 2db)

multiply second fraction by first denominator:
(d-b)/(d-b) * (d/b-d) = (-b^2 + db) / (-d^2 - b^2 + 2db)

You now have a common denominator:
(-d^2 +db) - (-b^2 + db) / (-d^2 - b^2 +2db)

Subtraction symbol acts as if you are multiplying the second fraction by -1:
-d^2 + db + b^2 - db / (-d^2 - b^2 + 2db)

Simplify:
-d^2 + b^2 / (-d^2 - b^2 +2db)