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The numerator is 2 less than the denominator. If I add 3 both to the numerator and the denominator, the answer would be 5/6. what's the original fraction? ​

User Zaxonov
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1 Answer

6 votes

Answer:


(7)/(9)

Explanation:

Let x be the denominator.

If the numerator is 2 less than the denominator, then the expression for the numerator is (x - 2):


(x-2)/(x)

If 3 is added to both the numerator and the denominator, and the answer is 5/6, then:


(x-2+3)/(x+3)=(5)/(6)

Now we can solve the equation for x.

Simplify the numerator in the fraction on the left of the equation:


(x+1)/(x+3)=(5)/(6)

Cross mutliply:


6(x+1)=5(x+3)

Expand the brackets:


6 \cdot x +6 \cdot 1 = 5 \cdot x + 5 \cdot 3


6x+6=5x+15

Subtract 5x from both sides of the equation:


6x+6-5x=5x+15-5x


x+6=15

Subtract 6 from both sides of the equation:


x+6-6=15-6


x=9

Therefore, the value of x is 9.

Now substitute the found value of x into the original rational expression:


(x-2)/(x)=(9-2)/(9)=(7)/(9)

Therefore, the original fraction is:


\boxed{(7)/(9)}

User Deejayy
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