Sum of numerator and denominator of a positive fraction is 8 if 2 is added to both numerator and denominator - Maths - Quadratic Equations

Question

Sum of numerator and denominator of a positive fraction is 8 if 2
is added to both numerator and denominator ,the fraction is
incresed by 4/35 Find the fraction I don't want any link

Koka Sri Lakshmi Divya Sai · Accepted Answer

Dear Student

Let the numerator be xand the denominator be yso,from the given datax+y=8⇒y=8-xand also givenx+2y+2-xy=435⇒xy+2y-xy-2xy(y+2)=435⇒2(y-x)y(y+2)=435⇒(y-x)y(y+2)=235⇒35y-35x=2y2+4y⇒2y2+4y=35y-8+y⇒2y2+4y=70y-280⇒2y2-66y+280=0⇒y2-33y+140=0⇒y2-5y-28y+140=0⇒yy-5-28y-5=0⇒y-5y-28=0⇒y=5,28Here we take y=5 as the fraction is positiveso x=8-yx=8-5=3So,the required fraction is 35
Regards

Sum of numerator and denominator of a positive fraction is 8.if 2 is added to both numerator and denominator ,the fraction is incresed by 4/35 . Find the fraction. I don't want any link.