Solve 6/x-3=3/x for x and determine if the solution is extraneous or not.

Question

Solve 6/x-3=3/x  for x and determine if the solution is extraneous or not.

mathmale · Answer

Are you dividing that 6 by x or are you dividing it by (x-3)?  Please use parentheses around the divisor(s) as necessary, so that there is no doubt regarding what comprises your divisor.

lovelycharm · Answer

is it non-extraneous or extraneous i got -3

lovelycharm · Answer

@mathmale

tkhunny · Answer

You first must answer the question.

 6/x-3=3/x

If you mean $\dfrac{6}{x} - 3 = \dfrac{3}{x}$, then you have written it correctly.

If you mean $\dfrac{6}{x-3} = \dfrac{3}{x}$, then parentheses are NOT optional.  You shoudl have written,  6/(x-3)=3/x

mathmale · Answer

@tkhunny:  Many thanks for reinforcing this!