limt→ 81[(81−t)/(9−√t)]=?

Question

81-t * 9 – root t
----------
9 – root t *9 – root t
=
81 – t (9 – rt t)
-------------------
81 – t
81 – t (9 – rt t) / -81
-------------------
81 – t / -81

81 – 9 – rt t
-------------------
81
/ -rt t
=9- rt t

where did i go wrong?

Answer 1

lim t→ 81 [(81−t)/(9−√t)]
= lim t→ 81 (9 - √t)(9 + √t) / (9 - √t)
= lim t→ 81 (9 + √t)
= 9 + 9 = 18

Answer 2

You made an error in the first step.
The first step should be
81 - t = (9+√t)(9−√t)