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

Question

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

Julia Adams · Accepted Answer

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

Abigail Allen · Answer

undefined To simplify the expression 1 / (((11x)sqrt5)-((3y)sqrt3)), we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is (((11x)sqrt5)+((3y)sqrt3)). This will eliminate the square roots in the denominator.

By applying the conjugate, the expression becomes:

1 / (((11x)sqrt5)-((3y)sqrt3)) * (((11x)sqrt5)+((3y)sqrt3)) / (((11x)sqrt5)+((3y)sqrt3))

Expanding the numerator and denominator, we get:

(1 * (((11x)sqrt5)+((3y)sqrt3))) / ((((11x)sqrt5)^2)-(((3y)sqrt3)^2))

Simplifying further:

(((11x)sqrt5)+((3y)sqrt3)) / (55x^2 - 9y^2)

Therefore, the simplified expression is (((11x)sqrt5)+((3y)sqrt3)) / (55x^2 - 9y^2).