Evaluate the limit (y-->3)

Evaluate the limit (y-->3) [sqrt(y^2+5y+1) - sqrt(y^2+3y+7)] / [y-3]

step by step please, i am lost.

[sqrt(y^2+5y+1) - sqrt(y^2+3y+7)] / [y-3]
Multiply [sqrt(y^2+5y+1) + sqrt(y^2+3y+7)]
to both the num. and den.

Recall (a+b)(a-b) = a^2-b^2

The num
= (y^2+5y+1) - (y^2+3y+7)
= 2y - 6

[sqrt(y^2+5y+1) - sqrt(y^2+3y+7)] / [y-3]
= (2y-6) / (y-3)[sqrt(y^2+5y+1) + sqrt(y^2+3y+7)]
= 2/ [sqrt(y^2+5y+1) + sqrt(y^2+3y+7)]

Take y to 3.
2/(sqrt25 + sqrt25)
= 2/10
=1/5

The limit does not exist....