已知x=4pq/(p+q) 求(x+2p)/(x-2p)+(x+2q)/(x-2q)的值

題目：

已知x=4pq/(p+q) 求(x+2p)/(x-2p)+(x+2q)/(x-2q)的值

解答：

∵x=4pq/(p+q)∴(p+q)x=4pq
∴(x+2p)/(x-2p)+(x+2q)/(x-2q)
=[(x+2p)(x-2q)+(x+2q)(x-2p)]/[x-2p)(x-2q)] (通分）
=[x²+2(p-q)x-4pq+x²+4(q-p)x-4pq]/[x²-2(p+q)x+4pq]
=(2x²-8pq)/(x²-8pq+4pq)
=2(x²-4pq)/(x²-4pq)
=2