what is the fraction

Question

numerator is one less than the denominator.if 3 is added to both numerator and denominator the fraction becomes 3/28 times the original. what is the fraction?

Answer 1

Original fraction: x/(x+1)

 

(x + 3)/(x+1+3) = (3/28)(x/(x+1))

 

(x+3)/(x+4) = 3x/(28(x+1))

 

3x(x+4) = 28(x+1)(x+3)

 

3x² + 12x = 28(x² + 4x + 3)

 

3x² + 12x = 28x² + 112x + 84

 

25x² + 100x + 84 = 0

 

using quadratic equation with a=25, b=100, c=84

 

x = [-100 ±√(100²-4(25(84))]/(2(25))

 

Can you finish working the quadratic?

Answer 2

These words describe the following situation:

 

fraction:  (x-1)/x

 

If modified: (x-2)/(x+3) = (3/28)[(x-1)/x]Solve this equation!