The denominator of a fraction is greater than the numerator by 3. If 7 is added to the numerator , the fraction increases by unity. Find the fraction.
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Let the numerator of fraction = x
denominator = x+3
fraction is \frac{x}{x+3}
if 7 is added to the numerator,the fraction increases by unity. Thus
\frac{x+7}{x+3}= \frac{x}{x+3}+1\\ \\ \Rightarrow \frac{x+7}{x+3}= \frac{x+x+3}{x+3}\\ \\ \Rightarrow \frac{x+7}{x+3}= \frac{2x+3}{x+3}\\ \\ \Rightarrow x+7=2x+3\\ \\ \Rightarrow x-2x=3-7\\ \\ \Rightarrow -x=-4\\ \\ \Rightarrow x=4
Fraction is \frac{x}{x+3}= \frac{4}{4+3}=\boxed{ \frac{4}{7} }
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answer is 4/7
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10/4 answer because 3+7 /4
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