Exercise 27 Page 265

To rationalize a fraction with a binomial denominator, we multiply the numerator and denominator of the fraction by the conjugate of the denominator.

-6-3sqrt(5)

Practice makes perfect

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 2+sqrt(5).

3/2-sqrt(5)

ExpandFrac

a/b=a * (2+sqrt(5))/b * (2+sqrt(5))

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

▼

Simplify numerator

Distr

Distribute 3

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

Multiply

6+3sqrt(5)/(2-sqrt(5))(2+sqrt(5))

ExpandDiffSquares

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

6+3sqrt(5)/2^2-(sqrt(5))^2

▼

Simplify denominator

CalcPow

Calculate power

6+3sqrt(5)/4-(sqrt(5))^2

PowSqrt

( sqrt(a) )^2 = a

6+3sqrt(5)/4-5

SubTerm

Subtract term

6+3sqrt(5)/-1

MoveNegDenomToNum

Put minus sign in numerator

-(6+3sqrt(5))/1

DivByOne

a/1=a

-(6+3sqrt(5))

Distr

Distribute -1

-6-3sqrt(5)

Subchapter links

1 Graphing Exponential Functions p.265

2 Solving Exponential Equations and Inequalities p.265

3 Simplifying Radical Expressions p.265

4 Operations with Radical Expressions p.266

5 Radical Equations p.266

Exercise 27 Page 265

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