已知x=4pq/(p+q) 求(x+2p)/(x-2p)+(x+2q)/(x-2q)的值
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已知x=4pq/(p+q) 求(x+2p)/(x-2p)+(x+2q)/(x-2q)的值
![已知x=4pq/(p+q) 求(x+2p)/(x-2p)+(x+2q)/(x-2q)的值](/uploads/image/z/16164270-54-0.jpg?t=%E5%B7%B2%E7%9F%A5x%3D4pq%2F%28p%2Bq%29+%E6%B1%82%28x%2B2p%29%2F%28x-2p%29%2B%28x%2B2q%29%2F%28x-2q%29%E7%9A%84%E5%80%BC)
∵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
∴(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
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