1. 3/2x=-2
3=-4x
x=-3/4
2. x/(x-1)+2/(x+1)=1
x(x+1)+2(x-1)=(x-1)(x+1)
x^2+x+2x-2=x^2-1
3x=1
x=1/3
3. 1/(x+1)-x^2/(x^2+3x+2)=-1
1/(x+1)-x^2/(x+1)(x+2)=-1
(x+2)/(x+1)(x+2)-x^2(x+1)(x+2)=-1
x+2-x^2=-(x+1)(x+2)
x^2-x-2=x^2+3x+2
4x=-4
x=-1
x/(2x-1)=(-2x-1)/(1-2x)
x=2x+1
x=-1
(3) (11-2x)/(4-x)=(1-x)/(x-4)
11-2x=x-1
3x=12
x=4
âµå½x=4æ¶,åæ¹ç¨æ æä¹,
â´åæ¹ç¨æ 解
7/ï¼x2+xï¼+3/(x2-x)=6/(x2-1)
解 æ¹ç¨ä¸¤è¾¹åä¹ä»¥æç®å
¬åæ¯xï¼x+1ï¼ï¼x-1ï¼,å¾
7ï¼x-1ï¼+3ï¼x+1ï¼=6x
å»æ¬å·,å¾ 7x-7+3x+3=6x
移项,å¾7x-6x+3x=7-3
å并å类项,å¾4x=4
ç³»æ°å1,å¾x=1
3/x-6/(1-x)-(x+5)/x(1-x)=0
解 æ¹ç¨ä¸¤è¾¹åä¹ä»¥æç®å
¬åæ¯xï¼1-xï¼,å¾
3ï¼1-xï¼-6x-(x+5)=0
å»æ¬å·,å¾ 3-3x-6x-x-5=0
å并å类项,å¾-10x=2
ç³»æ°å1,å¾x=-1/5
(5x-4)/(2x-4)=(2x+5)/(3x-6)-1/2
解 æ¹ç¨ä¸¤è¾¹åä¹ä»¥æç®å
¬åæ¯6ï¼x-2ï¼,å¾
3(5x-4)=2(2x+5)-3(x-2)
å»æ¬å·,å¾ 15x-12=4x+10-3x+6
移项,å¾15x-4x+3x=10+6+12
å并å类项,å¾14x=28
ç³»æ°å1,å¾x=2
ç»æ£éª,X=2æ¯å¢æ ¹,èå»,æ以åæ¹ç¨æ 解
x2-4x/(x2-1)+1=2x/(x+1)
解 æ¹ç¨ä¸¤è¾¹åä¹ä»¥æç®å
¬åæ¯(x2-1),å¾
x2-4x+x2-1=2x(x-1)
å³ 2x2-4x-1=2x2-2x
移项,å¾2x2-4x-2x2+2x=1
å并å类项,å¾-2x=1
x=-1/2
1/(x+3)+1/(6-2x)=(3x-15)/(2x2-18)
解 æ¹ç¨ä¸¤è¾¹åä¹ä»¥æç®å
¬åæ¯2(x+3)(x-3),å¾
2(x-3)-(x+3)=3x-15
å»æ¬å·,å¾2x-6-x-3=3x-15
移项,å¾2x-x-3x=-15+6+3
å并å类项,å¾-2x=-6
x=3
解å
³äºxçæ¹ç¨ï¼
x/(x-a)=1-[a/(x+b)] (aâ 0)
x/(x-a)+[a/(x+b)]=1
éå,ï¼x2+bx+ax-a2ï¼/[(x-a)(x+b)]=1
æ¹ç¨ä¸¤è¾¹åä¹ä»¥æç®å
¬åæ¯(x-a)(x+b),å¾
ï¼x2+bx+ax-a2ï¼=(x-a)(x+b)
å»æ¬å·,å¾x2+bx+ax-a2=x2+bx-ax-ab
移项,å¾x2+bx+ax-x2-bx+ax=-ab+a2
å并å类项,å¾2ax=a2-ab
x=(a-b)/2
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