Question 928782

{{{sqrt(2x)/(sqrt(8x)-sqrt(32))}}}=


{{{(sqrt(2x)(sqrt(8x)+sqrt(32)))/((sqrt(8x)-sqrt(32))(sqrt(8x)+sqrt(32)))}}}=


{{{(sqrt(2x)(sqrt(8x)+sqrt(32)))/(8x-32)}}}=


since {{{sqrt(2x)*sqrt(8x)=sqrt(16x^2)=4x}}} and {{{sqrt(32)=sqrt(4*4*2)=4sqrt(2)}}} , we have


{{{(4x+4sqrt(2)sqrt(2x))/(8x-32)}}}=


{{{cross(4)(x+sqrt(4x))/cross(4)(2x-8)}}}=


{{{(x+sqrt(4x))/(2x-8)}}}=


{{{(x+2sqrt(x))/(2x-8)}}}