Question

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

Answer 1

`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)`