Toán Lớp 8: Rút gọn biểu thức sau:
x+3 8x² 3x 1
A= 1+___________ : ( _________ – _________ – _____ )
(x+2)(x+3) 4x²(x-2) 3x² -12 x+2
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Comments ( 1 )
Giải đáp:
(x+4)/6
Lời giải và giải thích chi tiết:
ĐKXĐ: x\ne-3;x\ne±2;x\ne0
A=1+(x+3)/((x+2)(x+3)):((8x^2)/(4x^2(x-2))-(3x)/(3x^2-12)-1/(x+2))
=1+(x+3)/((x+2)(x+3)):[(8x^2)/(4x^2(x-2))-(3x)/(3(x^2-4))-1/(x+2)]
=1+(x+3)/((x+2)(x+3)):[(8x^2)/(4x^2(x-2))-(3x)/(3(x-2)(x+2))-1/(x+2)]
=1+(x+3)/((x+2)(x+3)):[(2)/(x-2)-(x)/((x-2)(x+2))-1/(x+2)]
=1+(x+3)/((x+2)(x+3)):[(2(x+2))/((x-2)(x+2))-(x)/((x-2)(x+2))-(x-2)/((x-2)(x+2))]
=1+(x+3)/((x+2)(x+3)):(2x+4-x-x+2)/((x-2)(x+2))
=1+1/(x+2):(6)/((x-2)(x+2))
=1+1/(x+2).((x-2)(x+2))/6
=1+(x-2)/6
=(6+x-2)/6
=(x+4)/6