Question

数学化简问题

计算[a^(4/3)-8a^(1/3)*b)/a^(2/3)+2a^(1/3)*b^(1/3)+4*b^(2/3)]除以[1-2(b/a)^1/3]
麻烦化简

Answer 1

[[a^(4/3)-8a^(1/3)*b)]/[a^(2/3)+2a^(1/3)*b^(1/3)+4*b^(2/3)]]
-----------------------------------------------------------
[1-2(b/a)^1/3]

[a^(4/3)-8a^(1/3)*b)]
= -------------------------------------------------------
[a^(2/3)+2a^(1/3)*b^(1/3)+4*b^(2/3)]*[1-2(b/a)^1/3]

设a^(1/3)=x,b^(1/3)=y,整理

[x^4-8*x*y^3]
= -----------------------------
[x^2+2xy+4y^2][1-2*y/x]

x[x^3-(2y)^3]
= ----------------------------- 分母立方差公式
[x^2+2xy+(2y)^2][x-2y]/x

x[x^3-(2y)^3]
= -----------------------
[x^3-(2y)^3]/x
=x^2
=a^(2/3)