Exercise 43 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.

35-7sqrt(3)/22

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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 5-sqrt(3).

7/5+sqrt(3)

ExpandFrac

a/b=a * (5-sqrt(3))/b * (5-sqrt(3))

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

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Distribute 7

Distr

Distribute 7

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

Multiply

35-7sqrt(3)/(5+sqrt(3))(5-sqrt(3))

ExpandDiffSquares

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

35-7sqrt(3)/5^2-(sqrt(3))^2

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Calculate power

CalcPow

Calculate power

35-7sqrt(3)/25-(sqrt(3))^2

PowSqrt

( sqrt(a) )^2 = a

35-7sqrt(3)/25-3

SubTerm

Subtract term

35-7sqrt(3)/22

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Exercises p.248-250

Exercise 43 Page 249

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