Rationalize the denominator and simplify. All variables represent positive real

Nann

Nann

Answered question

2021-09-20

Rationalize the denominator and simplify. All variables represent positive real numbers.
3y2x3y

Answer & Explanation

Isma Jimenez

Isma Jimenez

Skilled2021-09-21Added 84 answers

Rationalization is used to eliminate root radical in the denominator, for this both the numerator and denominator is multiplied by algebraic conjugate of denominator .For example if the denominator of an expression is a+b then the algebraic conjugate is ab. Now conjugate is multiplied to both numerator and denominator to get rationalized form of the expression.
In the given expression 3y2x3y the conjugate of denominator (2x3y) is (2x+3y)
To get the rationalize form multiply the numerator and denominator by (2x+3y)
Use the algebraic identity (a+b)(ab)=a2b2 to simplify the denominator
Apply product rule of exponent aman=am+n
3y2x3y=3y(2x+3y)(2x3y)(2x+3y)
=6xy+9y4x9y

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