what is the solution of (4/x+2)/(1/2x-8), please simplify it, THX! Salute!!!!

(4/x + 2) / ( (1/2)x - 8 ) =

[ (4 + 2x) / x ] / [ (1/2) ( x - 16) ] =

[ 2 (2) ( 2 + x) / x ] / (x - 16) =

[ 4(2 + x)] / [ x ( x - 16) ] =

[ 8 + 4x ] / [ x^2 - 16x) ]

question, sir, the original one is like this 4 over x plus 2 divided by 1 over 2x minus 8, so how can you separate out 1/2 and x because its like 1 divided 2x so im confused...

(4/x+2)/(1/2x-8) = \(\frac{\frac4x+2}{\frac12x-8}\)

Only the first number after the division sign goes in the denominator when there aren't parenthesees.

1/2x means 1/2 * x which is \(\frac12\) * x

and

1/(2x) means \(\frac1{2x}\)