How do you simplify # 1 / (((11x)sqrt5)-((3y)sqrt3))#?

1 Answer
Apr 25, 2017

Answer:

#1/(11xsqrt5-3ysqrt3)=(11xsqrt5+3ysqrt3)/(605x^2-27y^2)#

Explanation:

To simplify #1/(11xsqrt5-3ysqrt3)#, we should multiply numerator and denominator by conjugate of denominator i.e. #(11xsqrt5+3ysqrt3)#

Hence #1/(11xsqrt5-3ysqrt3)=(11xsqrt5+3ysqrt3)/((11xsqrt5-3ysqrt3)(11xsqrt5+3ysqrt3))#

= #(11xsqrt5+3ysqrt3)/((11xsqrt5)^2-(3ysqrt3)^2)#

= #(11xsqrt5+3ysqrt3)/((121x^2xx5)-(9y^2xx3))#

= #(11xsqrt5+3ysqrt3)/(605x^2-27y^2)#