Question 656308
Let {{{x}}} be the denominator.
Then, the numerator is {{{5x}}}, and the fraction is {{{5x/x}}}, which is equivalent to {{{5}}}.
{{{5x/x=5}}}
If you add {{{6}}} to both the numerator and the denominator, the resulting fraction is
{{{(5x+6)/(x+6)}}}
That fraction is equivalent to {{{2}}}, so we can write
{{{(5x+6)/(x+6)=2}}}
Multiplying both sides of the equal sign times {{{(x+6)}}} we get
{{{((5x+6)/(x+6))*(x+6)=2*(x+6)}}} --> {{{5x+6=2(x+6)}}} --> {{{5x+6=2x+2*6}}} --> {{{5x+6=2x+12}}}
Subtracting {{{2x}}} from both sides we get
{{{5x+6-2x=2x+12-2x}}} --> {{{3x+6=12}}}
Subtracting {{{6}}} from both sides we get
{{{3x+6-6=12-6}}} --> {{{3x=6}}}
Dividing both sides by 3 we get
{{{3x/3=6/3}}} --> {{{x=2}}}
So the original fraction was
{{{5x/x=5*2/2}}}
or {{{highlight(10/2)}}}