2013-11-10
展开全部
1)已知1/x-1/y=3,求x-3xy-y/2x+3xy-2y的值
(2)已知x+1/x =3,求x^2/x^4+x^2+1的值
(3)已知x/3=y/4=z/6≠0,求x+y-z/x-y+z的值
(4)计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4) (提示:应用拆项相消法,每一项都可拆成A-B/AB=1/B-1/A)
2 a+1-a+3 a2-4a-5÷a2-9 a2-3a-10.
解 原式=[x+2 x(x-2)-x-1(x-2)2]�6�1x 4-x (括号内分式的分母中的多项式式分解因式.分式的除法法则)
=[(x+2)(x-2)x(x-2)2-x(x-1)x(x-2)2]�6�1x4-x(异分母的分式减法的法则)
=x2-4-x2+x x(x-2)2�6�1x4-x (整式运算)
=x-4x(x-2)2�6�1x4-x (合并同类项)
=x-4 x(x-2)2�6�1(-xx-4) (分式的符号法则)
=-1(x-2)2. (分式的乘法法则)
计算x+y x2-xy +(x2-y2 x)2�6�1(1 y-x)3.
解 原式=x+y x(x-y)+(x+y)2(x-y)2x2�6�11(y-x)3
=x+y x(x-y)-(x+y)2 x2(x-y)
=x2+xy-x2-2xy-y2 x2(x-y)
=-xy-y2 x2(x-y)=-xy+y2 x2(x-y).
x-y+4xy x-y)(x+y-4xyx+y)
答案x2-y2
[1 (a+b)2-1(a-b)2]÷(1a+b-1a-b)
答案2a (a+b)(a-b);
x x-y�6�1 y2 x+y-x4y x4-y4÷x2 x2+y2
答案-xy x+y
3x-2 x2-x-2+(1-1x+1)÷(1+1x-1)
答案x2 (x+1)(x-2);
(2x x+1+2 x-1+4x x2-1)×(2x x+1+2 x-1-4x x2-1).
(2)已知x+1/x =3,求x^2/x^4+x^2+1的值
(3)已知x/3=y/4=z/6≠0,求x+y-z/x-y+z的值
(4)计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4) (提示:应用拆项相消法,每一项都可拆成A-B/AB=1/B-1/A)
2 a+1-a+3 a2-4a-5÷a2-9 a2-3a-10.
解 原式=[x+2 x(x-2)-x-1(x-2)2]�6�1x 4-x (括号内分式的分母中的多项式式分解因式.分式的除法法则)
=[(x+2)(x-2)x(x-2)2-x(x-1)x(x-2)2]�6�1x4-x(异分母的分式减法的法则)
=x2-4-x2+x x(x-2)2�6�1x4-x (整式运算)
=x-4x(x-2)2�6�1x4-x (合并同类项)
=x-4 x(x-2)2�6�1(-xx-4) (分式的符号法则)
=-1(x-2)2. (分式的乘法法则)
计算x+y x2-xy +(x2-y2 x)2�6�1(1 y-x)3.
解 原式=x+y x(x-y)+(x+y)2(x-y)2x2�6�11(y-x)3
=x+y x(x-y)-(x+y)2 x2(x-y)
=x2+xy-x2-2xy-y2 x2(x-y)
=-xy-y2 x2(x-y)=-xy+y2 x2(x-y).
x-y+4xy x-y)(x+y-4xyx+y)
答案x2-y2
[1 (a+b)2-1(a-b)2]÷(1a+b-1a-b)
答案2a (a+b)(a-b);
x x-y�6�1 y2 x+y-x4y x4-y4÷x2 x2+y2
答案-xy x+y
3x-2 x2-x-2+(1-1x+1)÷(1+1x-1)
答案x2 (x+1)(x-2);
(2x x+1+2 x-1+4x x2-1)×(2x x+1+2 x-1-4x x2-1).
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