[Form 5 Maths] Limit

lim (x - 7) / (√(x+2) - 3)
x-->7 =lim (x - 7)(√(x+2) + 3) / [(√(x+2) - 3) (√(x+2) + 3)]
x-->7 =lim (x - 7)(√(x+2) + 3) / (x - 7)
x-->7=lim √(x+2) + 3
x-->7= √(7+2) + 3= 6

☂雨後陽光☀ has used the method "Multiplication of conjugate surds" to both numerator and denominator, which is one approach you can adopt to solve the above problem in S.5 level. If you are clever, consider also L"Hospital's Rule for it is in 0/0 format.