中四mth
2007-10-29 4:50 am
in a fraction,the numerator is less then the denominator by 3 . when both the numerator and the denominator are increased by 2, the fraction is increased by 1/20 . find the orginal fraction.
回答 (2)
2007-10-29 5:00 am
✔ 最佳答案
Let the original fraction be ( x - 3 ) / x, so( x - 3 + 2 ) / ( x + 2 ) = ( x - 3 ) / x + 1 / 20
( x - 1 ) / ( x + 2 ) = ( x - 3 ) / x + 1 / 20
x ( x - 1 ) = ( x - 3 )( x + 2 ) + x ( x + 2 ) / 20
20x^2 - 20x = 20 ( x^2 - x - 6 ) + x^2 + 2x
20x^2 - 20x = 20x^2 - 20x - 120 + x^2 + 2x
x^2 + 2x - 120 = 0
( x + 12 )( x -10 ) = 0
x = -12 ( rejected ) or x = 10
So the original fraction is 7 / 10.
參考: My Maths Knowledge
2007-10-30 5:14 am
The original fraction is 7 / 10.
收錄日期: 2021-04-13 18:45:04
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