Exercise 48 Page 249

To rationalize a fraction with a binomial denominator, we multiply 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 2sqrt(7)-3sqrt(3).

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

ExpandFrac

a/b=a * (2sqrt(7)-3sqrt(3))/b * (2sqrt(7)-3sqrt(3))

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

▼

Distribute 2sqrt(5)

Distr

Distribute 2sqrt(5)

4sqrt(5)* sqrt(7)-6sqrt(5)* sqrt(3)/(2sqrt(7)+3sqrt(3))(2sqrt(7)-3sqrt(3))

ProdSqrt

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

4sqrt(5* 7)-6sqrt(5* 3)/(2sqrt(7)+3sqrt(3))(2sqrt(7)-3sqrt(3))

Multiply

Multiply

4sqrt(35)-6sqrt(15)/(2sqrt(7)+3sqrt(3))(2sqrt(7)-3sqrt(3))

ExpandDiffSquares

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

4sqrt(35)-6sqrt(15)/(2sqrt(7))^2-(3sqrt(3))^2

▼

Calculate power

PowProdII

(a b)^m=a^m b^m

4sqrt(35)-6sqrt(15)/2^2(sqrt(7))^2-3^2(sqrt(3))^2

CalcPow

Calculate power

4sqrt(35)-6sqrt(15)/4(sqrt(7))^2-9(sqrt(3))^2

PowSqrt

( sqrt(a) )^2 = a

4sqrt(35)-6sqrt(15)/4(7)-9(3)

Multiply

Multiply

4sqrt(35)-6sqrt(15)/28-27

SubTerm

Subtract term

4sqrt(35)-6sqrt(15)/1

DivByOne

a/1=a

4sqrt(35)-6sqrt(15)