Toán Lớp 8: $(\frac{1}{1-x}-1): (x-\frac{1-2x}{1-x}-1)$
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Toán Lớp 8: $(\frac{1}{1-x}-1): (x-\frac{1-2x}{1-x}-1)$
Comments ( 2 )
( 1/(1-x) – 1):(x – (1-2x)/(1-x) – 1)
<=> ( (1 – 1 + x)/(1-x) ):( [x.(1-x) – 1 + 2x – 1.(1-x)]/(1-x) )
<=> x/(1-x) : (x – x^2 – 1 + 2x – 1 + x)/(1-x)
<=> x/(1-x) : (-x^2 + 4x – 2)/(1-x)
<=> x/(1-x) . (1-x)/(-x^2 + 4x – 2)
<=> x/(-x^2 + 4x – 2)
(1/(1-x)-1):(x-(1-2x)/(1-x)-1)
=(1/(1-x)-(1-x)/(1-x)):[(x-1)+(1-2x)/(x-1)]
=(1/(1-x)+(x-1)/(1-x)):[(x-1)^2/(x-1)+(1-2x)/(x-1)]
=(1+x-1)/(1-x):(x^2-2x+1+1-2x)/(x-1)
=(x)/(1-x):(x^2-4x+2)/(x-1)
=(-x)/(x-1).(x-1)/(x^2-4x+2)
=(-x)/(x^2-4x+2)