3.80: Intersection of curve and line; shaded area

0606/12/F/M/25 — Question 7 · 10 marks

3.80 diagram
(a)
The diagram shows part of the curve y=5x+1+2y=\dfrac{5}{x+1}+2 and part of the line y=2x+1y=2x+1 intersecting at AA.
Find the coordinates of AA.
[4]
(b)
Find the exact area of the shaded region.
[6]