The numerator of a rational number is 7 less than the denominator. if the denominator is increased by 9and the numerator by 2, we get the same rational number.find the number.
Answers
Answered by
29
= x - 7/x
= x-7+12/x+9
= x+5 = x-9
= 2x = -9-5
= x = -14/2
x = -7
= x-7+12/x+9
= x+5 = x-9
= 2x = -9-5
= x = -14/2
x = -7
Answered by
54
Define x:
Let the numerator be x
The denominator is x + 7
Define the fraction:
The fraction is x/(x + 7)
Solve x:
The denominator increased by 9 and numerator decreased by 2, we can the same number
(x + 2) / ( x+ 7 + 9) = x / (x + 7)
(x + 2) / ( x+ 16) = x / (x + 7)
(x + 2) ( x + 7) = x (x + 16)
x² + 9x + 14 = x² + 16x
16x - 9x = 14
7x = 14
x = 2
Find the fraction:
Numerator = x = 2
denominator = x + 7 = 2 + 7 = 9
Find the fraction:
Fraction = 2/9
Answer: The fraction is 2/9
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