Question

what is 17-12√2+3-2√2/3-2√2

Answer 1

(17-12√2+3-2√2) / 3-2√2  is given 
by solving, we get 
(17-12√2+3-2√2) / 3-2√2 = (20-14√2) / 3-2√2

By rationalising the denominator in (20-14√2) / 3-2√2
              = [(20-14√2) / (3-2√2)] × [(3+2√2) / (3+2√2)]
              = (20-14√2)(3+2√2) / (3+2√2)(3-2√2) ---- 1

We know that, 
(3+2√2)(3-2√2) = 9-8 = 1
placing in 1
             = (20-14√2)(3+2√2) / 1
             = 60+40√2-42√2-54
             = 6-2√2 is the answer

Answer 2

17-12√2+3-2√2/3-2√2
=17+3-√2(12+2)/3-2√2
=20-14√2/3-2√2
now we know (3-2√2)*(3+2√2)=9-8=1
Therefore multiplying numerator and denominator by 3+2√2 we get,
=4-2√2/1
=4-2√2