Jika p=(x^(4/3)+x^(1/3))(x^(-1/6)-x^(-2/3)) dan

x^(-2/3) * (x^(1/2) - 1) / (x^(5/6) - 1)

Pembahasan

Untuk menyelesaikan soal ini, kita perlu menyederhanakan ekspresi p dan q terlebih dahulu, kemudian mencari nilai p/q.

p = (x^(4/3) + x^(1/3))(x^(-1/6) - x^(-2/3))
Kita bisa memfaktorkan x^(1/3) dari suku pertama dan x^(-2/3) dari suku kedua:
p = x^(1/3) * (x + 1) * x^(-2/3) * (x^(3/6) - 1)
p = x^(1/3 - 2/3) * (x + 1) * (x^(1/2) - 1)
p = x^(-1/3) * (x + 1) * (x^(1/2) - 1)

q = (x^(2/3) + x^(-1/3))(x^(7/6) - x^(2/3))
Kita bisa memfaktorkan x^(-1/3) dari suku pertama dan x^(2/3) dari suku kedua:
q = x^(-1/3) * (x + 1) * x^(2/3) * (x^(5/6) - 1)
q = x^(-1/3 + 2/3) * (x + 1) * (x^(5/6) - 1)
q = x^(1/3) * (x + 1) * (x^(5/6) - 1)

Sekarang kita hitung p/q:
p/q = [x^(-1/3) * (x + 1) * (x^(1/2) - 1)] / [x^(1/3) * (x + 1) * (x^(5/6) - 1)]
p/q = x^(-1/3 - 1/3) * (x^(1/2) - 1) / (x^(5/6) - 1)
p/q = x^(-2/3) * (x^(1/2) - 1) / (x^(5/6) - 1)

Nilai p/q = x^(-2/3) * (x^(1/2) - 1) / (x^(5/6) - 1).