lim x->1 [(sqrt10-x)-3]/[1-(1/x)] Help please, Thankyou

Answer 1

First multiply top and bottom by x/x

= lim x(√(10-x) - 3)/(x-1)
multiply top and bottom by (√(10-x) + 3)/(√(10-x) + 3)

to get
x(√(10-x) - 3)/(x-1) * (√(10-x) + 3)/(√(10-x) + 3)
= x( 10-x - 9)((x-1)(√(10-x) + 3))
= x(1-x)/((x-1)(√(10-x) + 3)
= -x/(√(10-x) + 3)

and as x ---> 1 we get

-1/(√9+3) = -1/6