McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
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Exercise 28 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. We find the conjugate by changing the sign of the second term of the expression.

5sqrt(7)-30/-29

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 sqrt(7)-6.
5/sqrt(7)+6
5(sqrt(7)-6)/(sqrt(7)+6)(sqrt(7)-6)
â–Ľ
Simplify numerator
5sqrt(7)-5(6)/(sqrt(7)+6)(sqrt(7)-6)
5sqrt(7)-30/(sqrt(7)+6)(sqrt(7)-6)
5sqrt(7)-30/(sqrt(7))^2-6^2
â–Ľ
Simplify denominator
5sqrt(7)-30/(sqrt(7))^2-36
5sqrt(7)-30/7-36
5sqrt(7)-30/-29