Rationalise denominator

Question 1

So how does it work?

15/[3] + [48] in form b[3]

Answer 1

U just times by the surd e.g.

15/[3] x [3]/[3] = 15[3]/3 = 5[3]

[48] = [3][16] = 4[3]+5[3] = 9[3]

(factors of 48 with 1 that can be rooted =
3, 16)

Question 2

But what about this harder one!?!?!?

5/4+[3] <– rationalise that one

Answer 2

So u rationalise with that whole denominator but u must swap the signs cuz ye e.g.

5/4+[3] x 4-[3]/4-[3]

(stuff at bottom is like expanding:)
(4+[3])(4-[3])
=16-4[3]+4[3]-3
16-3=13

So then:
5(4-[3])/13 =
20-5[3]/13