分式的乘除.···(1)x²分之x²+x乘x²-1分之x (2) x²-3x分之
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分式的乘除.···
(1)x²分之x²+x乘x²-1分之x (2) x²-3x分之x÷x²-9分之1 (3)x²-3x分之x÷x²-9分之1 (4) x²-1分之x²-2x+1÷x²+x分之x-1
(1)x²分之x²+x乘x²-1分之x (2) x²-3x分之x÷x²-9分之1 (3)x²-3x分之x÷x²-9分之1 (4) x²-1分之x²-2x+1÷x²+x分之x-1
(1)x²分之x²+x乘x²-1分之x
=(x²+x)/x²*x/(x²-1)
=x(x+1)/x²*x/[(x+1)(x-1)]
=1/(x-1)
(2) x²-3x分之x÷x²-9分之1
=x/(x²-3x)÷1/(x²-9)
=x/x(x-3)*(x²-9)
=1/(x-3)*(x+3)(x-3)
=x+3
(3)x²-3x分之x÷x²-9分之1
=x/(x²-3x)÷1/(x²-9)
=x/x(x-3)*(x²-9)
=1/(x-3)*(x+3)(x-3)
=x+3
(4) x²-1分之x²-2x+1÷x²+x分之x-1
=(x²-2x+1)/(x²-1)÷(x-1)/(x²+x)
=(x-1)²/(x+1)(x-1)*(x²+x)/(x-1)
=(x-1)/(x+1)*x(x+1)/(x-1)
=x
=(x²+x)/x²*x/(x²-1)
=x(x+1)/x²*x/[(x+1)(x-1)]
=1/(x-1)
(2) x²-3x分之x÷x²-9分之1
=x/(x²-3x)÷1/(x²-9)
=x/x(x-3)*(x²-9)
=1/(x-3)*(x+3)(x-3)
=x+3
(3)x²-3x分之x÷x²-9分之1
=x/(x²-3x)÷1/(x²-9)
=x/x(x-3)*(x²-9)
=1/(x-3)*(x+3)(x-3)
=x+3
(4) x²-1分之x²-2x+1÷x²+x分之x-1
=(x²-2x+1)/(x²-1)÷(x-1)/(x²+x)
=(x-1)²/(x+1)(x-1)*(x²+x)/(x-1)
=(x-1)/(x+1)*x(x+1)/(x-1)
=x
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