.If numerator of fraction is 3 less than its denominator. If we add 4 to numerator and reduce 3 from denominator then fraction becomes 3/1. find the fraction.
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Let the denominator be x then numerator be (x-3)
fraction =xx−3
It is added ⇒x+1x−3=xx−3−151 (by the condition)
⇒x+1x−3=15x15x−45−x.
⇒x+1x−3=15x14x−45
⇒15x2−45x=14x2−45x+14x−45
⇒x2−14x+45=0
⇒x2−9x−5x+45=0
⇒x(x−9)−5(x−9)=0
⇒x−5=0,x−9=0
∴x=5,9.
If x = 9 ⇒ fraction =99−3
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