math F4 Help

2011-02-04 12:52 pm
化簡1/1-x +( (x-4)(x+2)/16-x^2) / ( (x^2+2x)/x^2+4x))

回答 (1)

2011-02-04 9:35 pm
✔ 最佳答案
1/(1-x) + ((x-4)(x+2)/(16-x²) / ((x²+2x)/(x²+4x))
= 1/(1-x) + ((x-4)(x+2)/((4-x)(4+x)) / ((x²+2x)/(x²+4x))
= 1/(1-x) - ((x+2)/(x+4)) / ((x²+2x)/(x²+4x))
= 1/(1-x) - ((x+2)/(x+4)) / ( x(x+2)/(x(x+4)) )
= 1/(1-x) - 1
= 1/(1-x) - (1-x)/(1-x)
= x / (1 - x)


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