Question 1120905
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Using formal algebra....<br>
Let the original fraction be {{{x/(x+2)}}}.<br>
3 subtracted from both numerator and denominator makes the fraction {{{(x-3)/(x-1)}}}.<br>
We want that new fraction to have the value 3/4:<br>
{{{(x-3)/(x-1) = 3/4}}}
{{{3x-3 = 4x-12}}}
{{{x = 9}}}<br>
The original fraction is x/(x+2) = 9/11.<br>
Using logical reasoning....<br>
When 3 is subtracted from both numerator and denominator, the numerator is still 2 less than the denominator.  So look for a fraction equivalent to 3/4 in which the numerator is 2 less than the denominator.<br>
In the fraction 3/4, the numerator is 1 less than the denominator; multiplying numerator and denominator by 2 will give us a fraction equivalent to 3/4 in which the numerator is 2 less than the denominator: 3/4 = 6/8.<br>
So 6/8 is the fraction after 3 has been subtracted from both numerator and denominator; that means the original fraction was 9/11.