Exercise 5 Page 964

We want to find a simpler form of the given fraction with a binomial denominator. To do it, we will rationalize the fraction by multiplying the numerator and denominator of the fraction by the conjugate of the denominator. We find the conjugate by changing the sign of the second term of the expression.

Binomial	Conjugate
a + b	a - b
a - b	a + b

In this case, the conjugate of the denominator is 3+sqrt(2).

sqrt(5)/3-sqrt(2)

ExpandFrac

a/b=a * (3+sqrt(2))/b * (3+sqrt(2))

sqrt(5)(3+sqrt(2))/(3-sqrt(2))(3+sqrt(2))

(a-b)(a+b)=a^2-b^2

sqrt(5)(3+sqrt(2))/9-(sqrt(2))^2

PowSqrt

( sqrt(a) )^2 = a

sqrt(5)(3+sqrt(2))/9-2

SubTerm

Subtract term

sqrt(5)(3+sqrt(2))/7

Distr

Distribute sqrt(5)

3sqrt(5)+sqrt(2)sqrt(5)/7

ProdSqrt

sqrt(a)*sqrt(b)=sqrt(a* b)

3sqrt(5)+sqrt(2* 5)/7

Multiply

Multiply

3sqrt(5)+sqrt(10)/7

This corresponds to option D.