Question

Rationalize the numerator. $$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$

   Rationalize the numerator.
$$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$

Precalculus

Robert Blitzer 6th Edition

Chapter 0, Problem 81

Instant Answer

Solved by Expert Charles Machakwa

08/25/2021

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Step 1: We start with the given expression: $$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$ Show more…

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Rationalize the numerator. $$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$

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Key Concepts

Rationalization

Rationalization is an algebraic technique used to eliminate radicals from the numerator (or denominator) of an expression. This is typically achieved by multiplying the expression by a form of 1 that involves the conjugate of the radical-containing term, thereby simplifying the overall expression.

Conjugate

The conjugate is formed by changing the sign between two terms in a binomial. When an expression contains a sum or difference involving radicals, its conjugate is used in multiplication to take advantage of the difference of squares formula, which helps eliminate the radical terms.

Difference of Squares

The difference of squares is an algebraic identity where the product of two conjugate expressions results in the difference between the squares of the individual terms. This identity is particularly useful when rationalizing expressions because it converts a product of radicals into a difference of non-radical squared terms.

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