請化簡以下題目

[(y^3 + x^3)/(y^3 x^3)]
------------------------------
[(y+x)/yx]

(y^3 + x^3) yx
= --------------- * -----------
(y^3 x^3) (y + x)

(y^3 + x^3) yx
= --------------- * -------------
(y + x) (y^3 x^3)

(y + x)(y^2 - xy+ x^2) yx
= --------------------------- * -------------
(y + x) (y^3 x^3)

(y^2 – xy + x^2) 1
= --------------------- * -------------
1 (y^2 x^2)


y^2 – xy + x^2
= ---------------------------
(y^2 x^2)


Comment:
Factoring sum of cubes

y^3 + x^3 = (y + x)(y^2 – xy + x^2) Right

Note: There is a minus sign in front of xy


y^3 + x^3 = (y + x)(y^2 + xy + x^2) Wrong

圖片參考：http://imgcld.yimg.com/8/n/HA00704496/o/701101140150713873369600.jpg

Hope I can help you!!

(y^3+x^3)/(y^3)(x^3)/y+x/yx
=

圖片參考：http://www3.wolframalpha.com/Calculate/MSP/MSP580519e16786dg82gebe000010674e4h33c07584?MSPStoreType=image/gif&s=25&w=125&h=43

=

圖片參考：http://www3.wolframalpha.com/Calculate/MSP/MSP580819e16786dg82gebe00002448eed3i3cdaadh?MSPStoreType=image/gif&s=25&w=108&h=44

=

圖片參考：http://www3.wolframalpha.com/Calculate/MSP/MSP581419e16786dg82gebe0000428ig169a3261f2f?MSPStoreType=image/gif&s=25&w=86&h=44

[(y^3 + x^3)/(y^3 x^3)]/[(y+x)/yx]
= (y^3 + x^3)/x^3 y^3 * xy/(y+x)
= (x^3 + y^3)/(x+y) * xy/x^3 y^3
= (x+y)(x^2+xy+y^2)/(x+y) * 1/x^2 y^2
= (x^2 + xy + y^2)/x^2 y^2