in a fraction if 1 is added to both the numerator and the denomenator, the fraction becomes 1/2. if the?

Question

numerator is subtracted from the denominator, the fraction becomes 3/4. find the fraction.

Answer 1

You have a fraction of two numbers, call them a and b. You know that (a+1)/(b+1) = 1/2 and a/(b-a) = 3/4. Simplifying the first equation:

a+1=b/2+1/2
a-b/2=-1/2
2a-b=-1

And the second:

a=3/4 (b-a)
4a/3=b-a
7a/3-b=0
7a-3b=0

Subtracting 3 times the first equation from the second:

7a-3b - 3(2a-b) = 3
a=3

Substituting into the second equation, we find that b=7. So the fraction is 3/7.

Answer 2

let:
x be the numerator
y be the denominator
hence the fraction x/y

eq1: if 1 is added to both the resulting fraction is equal to 1/2.
x+1 / y + 1 = 1/2 -----cross multiply
2(x+1) = y+1
2x + 2 = y + 1 -----simplify
2x - y = -1 or
y = 2x + 1 ---equation1

eq2:if the numerator is subtracted from the denominator the fraction wil become 3/4.

x / (y-x) = 3/4 cross multiply
4x = 3(y-x)
4x = 3y - 3x ----simplify
7x - 3y = 0

use equation1 do substitution method
7x - 3(2x + 1) = 0
7x - 6x - 3 = 0
x -3 = 0
x = 3//

y = 2x + 1
y = 2(3) + 1
y= 7//

fraction is x/y =3/7 //answer!

Answer 3

This is the Inversion complex and one is dominate. Then answer is always 1.
Yea, took me years to prove this as teachers could not believe. But, since the majority of people have been taught different we still use the incorrect method to solve,