The difference 7

The difference between a proper fraction and its reciprocal is 7/12. Find the fraction.

Correct answer:

x =  -3/4

Step-by-step explanation:

x−x1​ = 127​ x2−1 = 127​⋅ x  12x2−7x−12=0  12x2−7x−12=0  a=12;b=−7;c=−12 D=b2−4ac=72−4⋅12⋅(−12)=625 D>0  x1,2​=2a−b±D​​=247±625​​ x1,2​=247±25​ x1,2​=0.291667±1.041667 x1​=1.333333333 x2​=−0.75  <1 x1​>1  x=x2​=(−0.75)=−43​=−0.75  Verifying Solution:   w = x−x1​ w=4−3​−3−4​=12−9​−12−16​=12−9+16​=127​≐0.5833

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