Urgent Questions (4) ^_^

1. Rationalize the following expressions.
(a) 2√3÷3√2=2√3√2÷3√2√2=2√6÷6=√6÷3
(b) 1÷√5- 2=√5÷5-2=√5÷5-10÷5=(√5-10)÷5
(c) 2÷√5+ √3=2√5÷5+5√3÷5=(2√5+5√3)÷5
(d) 1÷√3+√2 - 1÷√2 +1=√3÷3+3√2 ÷3-√2÷2+1=(√3+3√2 )÷3-√2÷2+1
=2(√3+3√2 )÷6-3√2÷6+6/6
=(2√3+6√2-3√2+6)÷6=(2√3+3√2+6)÷6

2. Use the simplest method to finish these questions, but you need to show the step clearly.
(a) Expand (√5 + √3 + √2)(√5 - √3 - √2).
(√5 + √3 + √2)(√5 - √3 - √2)=[√5 + (√3 + √2)][√5 - (√3 + √2)]
=5- (√3 + √2) (√3 + √2)=5- (3 +2+ 2√6)=5-5-2√6= -2√6
(b) Hence, rationalize -24÷√5 + √3 + √2. (Hint: multiply the number by (√5 - √3 - √2)÷(√5 - √3 - √2).
-24÷(√5 + √3 + √2)=[-24(√5 - √3 - √2)]÷[(√5 + √3 + √2)(√5 - √3 - √2]
=[-24(√5 - √3 - √2)]÷ (-2√6)=12(√5 - √3 - √2)÷ √6=12√6(√5 - √3 - √2)÷ 6
=2√6(√5 - √3 - √2)