# algebra

The denominator of a fraction is 4 less than the numerator .If the denominator is doubled and the numerator is increased by 6,the sum of the original fraction and the new one is 3 .Find the original fraction.

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1. original fraction --- x/(x-4)

new fraction = (x+6)/(2x-8)

x/(x-4) + (x+6)/(2x-8) = 3
2x/(2x-8) + (x+6)/(2x-8) = 3
(3x+6)/(2x-8) = 3
cross-multiply ....
6x-24 = 3x+6
3x=30
x=10

original fraction is 10/6

check:
old fraction = 10/6
new fraction = 16/12

10/6 + 16/12 = 20/12+16/12=36/12=3

btw, I think this is not a well thought-out question.
the problem only works if you leave your fractions in unsimplified form, most "mathematicians" would have reduced 10/6 to 5/3
once that is done, following the above steps would result in a negative fraction

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2. The numerator of a fraction is 7 less than the denominator.If the numeratoris increased by 2 and the denominator by 9,we again get the same fraction.find the fraction

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