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分解因式题1.(3-x/x^2-10x+25)/(x^2+2x-15/x^2-2x-15)*(x^2-25)2.(a^2+7a+12/a^2-8a+15)/(a^2+3a-4/a^2-5a+6)/(a^2+a-6/a^2-4a-5)
题目详情
分解因式题
1.(3-x/x^2-10x+25)/(x^2+2x-15/x^2-2x-15)*(x^2-25)
2.(a^2+7a+12/a^2-8a+15)/(a^2+3a-4/a^2-5a+6)/(a^2+a-6/a^2-4a-5)
1.(3-x/x^2-10x+25)/(x^2+2x-15/x^2-2x-15)*(x^2-25)
2.(a^2+7a+12/a^2-8a+15)/(a^2+3a-4/a^2-5a+6)/(a^2+a-6/a^2-4a-5)
▼优质解答
答案和解析
1.(3-x/x^2-10x+25)/(x^2+2x-15/x^2-2x-15)*(x^2-25)
=[(3-x)/(x-5)^2]/[(x+5)(x-3)/(x-5)(x+3)]*[(x-5)(x+5)]
=[(3-x)(x-5)(x+3)]/[(x-5)^2(x+5)(x-3)]*[(x-5)(x+5)]
=-[(x+3)(x-5)(x+5)]]/[(x-5)(x+5)]
=-x-3
2.(a^2+7a+12/a^2-8a+15)/(a^2+3a-4/a^2-5a+6)/(a^2+a-6/a^2-4a-5)
=[(a+3)(a+4)/(a-3)(a-5)]/[(a+4)(a-1)/(a-2)(a-3)]/[(a-2)(a+3)/(a-5)(a+1)]
=[(a+3)(a+4)(a-2)(a-3)]/[(a-3)(a-5)(a+4)(a-1)]/[(a-2)(a+3)/(a-5)(a+1)]
=[(a+3)(a-2)]/[(a-5)(a-1)]/[(a-2)(a+3)/(a-5)(a+1)]
=[(a+3)(a-2)(a-5)(a+1)]/[(a-5)(a-1)(a-2)(a+3)]
=(a+1)/(a-1)
=[(3-x)/(x-5)^2]/[(x+5)(x-3)/(x-5)(x+3)]*[(x-5)(x+5)]
=[(3-x)(x-5)(x+3)]/[(x-5)^2(x+5)(x-3)]*[(x-5)(x+5)]
=-[(x+3)(x-5)(x+5)]]/[(x-5)(x+5)]
=-x-3
2.(a^2+7a+12/a^2-8a+15)/(a^2+3a-4/a^2-5a+6)/(a^2+a-6/a^2-4a-5)
=[(a+3)(a+4)/(a-3)(a-5)]/[(a+4)(a-1)/(a-2)(a-3)]/[(a-2)(a+3)/(a-5)(a+1)]
=[(a+3)(a+4)(a-2)(a-3)]/[(a-3)(a-5)(a+4)(a-1)]/[(a-2)(a+3)/(a-5)(a+1)]
=[(a+3)(a-2)]/[(a-5)(a-1)]/[(a-2)(a+3)/(a-5)(a+1)]
=[(a+3)(a-2)(a-5)(a+1)]/[(a-5)(a-1)(a-2)(a+3)]
=(a+1)/(a-1)
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