Toán Lớp 8: Rút gọn biểu thức :
$\frac{2}{x(x-2)}$ + $\frac{2}{(x-2)(x-4)}$ +…+$\frac{2}{(x-2020)(x-2022)}$
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Toán Lớp 8: Rút gọn biểu thức :
$\frac{2}{x(x-2)}$ + $\frac{2}{(x-2)(x-4)}$ +…+$\frac{2}{(x-2020)(x-2022)}$
Comments ( 2 )
Giải đáp:
2022/(x(x-2022))
Lời giải và giải thích chi tiết:
2/(x(x-2)) + 2/((x-2)(x-4)) + …. + 2/((x-2020)(x-2022))
= 1/(x – 2) – 1/x + 1/(x – 4) – 1/(x – 2) + …. + 1/(x – 2022) – 1/(x – 2020)
= -1/x + ( 1/(x – 2) – 1/(x – 2) ) + ( 1/(x – 4) – 1/(x – 4) ) + …. + ( 1/(x – 2020) – 1/(x – 2020) ) + 1/(x – 2022)
= -1/x + 1/(x – 2022)
= ( -(x – 2022) + x)/( x(x – 2022) )
= ( -x + 2022 + x)/( x(x – 2022) )
= 2022/( x(x – 2022) )
2/(x(x-2))+2/((x-2)(x-4))+…+2/((x-2020)(x-2022))
=(x-x+2)/(x(x-2))+ (x-2-x+4)/((x-2)(x-4)) + … + (x-2020-x+2022)/((x-2020)(x-2022))
= 1/(x-2) – 1/x + 1/(x-4) -1/(x-2)+…+1/(x-2022)-1/(x-2020)
=-1/x + 1/(x-2022)
= (-x+2022+x)/(x(x-20222))
=2022/(x(x-2022))