解答下列各题：（1）分解因式：4a2-8ab+4b2-16c2（2）计算：（2a+b）（2a-b）+b（2a+b）-8a2b÷2b（3）化简求值：（3x+4x2-1-2x-1）÷x+2x2-2x+1，其中x=-3（4）解分式方程：xx-2-1=8x2-4．

Question

解答下列各题：
（1）分解因式：4a²-8ab+4b²-16c²
（2）计算：（2a+b）（2a-b）+b（2a+b）-8a²b÷2b
（3）化简求值：（(3x+4)/(x2-1)-(2)/(x-1)）÷(x+2)/(x2-2x+1)，其中x=-3
（4）解分式方程：(x)/(x-2)-1=(8)/(x2-4)．
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2
(3x+4)/(x2-1)-(2)/(x-1)）÷(x+2)/(x2-2x+1)，其中x=-3
（4）解分式方程：(x)/(x-2)-1=(8)/(x2-4)．(3x+4)/(x2-1)3x+4x2-13x+43x+4x2-1x2-1x2-1x2-12-1(2)/(x-1)）÷(x+2)/(x2-2x+1)，其中x=-3
（4）解分式方程：(x)/(x-2)-1=(8)/(x2-4)．(2)/(x-1)2x-122x-1x-1(x+2)/(x2-2x+1)，其中x=-3
（4）解分式方程：(x)/(x-2)-1=(8)/(x2-4)．(x+2)/(x2-2x+1)x+2x2-2x+1x+2x+2x2-2x+1x2-2x+1x2-2x+1x2-2x+12-2x+1
(x)/(x-2)-1=(8)/(x2-4)．(x)/(x-2)xx-2xxx-2x-2(8)/(x2-4)．(8)/(x2-4)8x2-488x2-4x2-4x2-4x2-42-4

Answer 1

（1）原式=4（a²2-2ab+b²2-4c²2）
=4[（a²2-2ab+b²2）-4c²2]=4[（a-b）²2-4c²2]
=4（a-b+2c）（a-b-2c）；
（2）原式=4a⁴4-b²2+2ab+b²2-4a²2=2ab；
（3）原式=[(3x+4)/((x+1)(x-1))-(2)/(x-1)]÷(x+2)/((x-1)2)
=(3x+4)/((x+1)(x-1))•((x-1)2)/(x+2)-(2)/(x-1)•((x-1)2)/(x+2)
=((3x+4)(x-1))/((x-1)(x+2))-(2(x-1)2)/((x-1)(x+2))
=((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． (3x+4)/((x+1)(x-1))3x+4(x+1)(x-1)3x+43x+43x+4(x+1)(x-1)(x+1)(x-1)(x+1)(x-1)-(2)/(x-1)]÷(x+2)/((x-1)2)
=(3x+4)/((x+1)(x-1))•((x-1)2)/(x+2)-(2)/(x-1)•((x-1)2)/(x+2)
=((3x+4)(x-1))/((x-1)(x+2))-(2(x-1)2)/((x-1)(x+2))
=((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． (2)/(x-1)2x-1222x-1x-1x-1]÷(x+2)/((x-1)2)
=(3x+4)/((x+1)(x-1))•((x-1)2)/(x+2)-(2)/(x-1)•((x-1)2)/(x+2)
=((3x+4)(x-1))/((x-1)(x+2))-(2(x-1)2)/((x-1)(x+2))
=((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． (x+2)/((x-1)2)x+2(x-1)2x+2x+2x+2(x-1)2(x-1)2(x-1)22
=(3x+4)/((x+1)(x-1))•((x-1)2)/(x+2)-(2)/(x-1)•((x-1)2)/(x+2)
=((3x+4)(x-1))/((x-1)(x+2))-(2(x-1)2)/((x-1)(x+2))
=((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． (3x+4)/((x+1)(x-1))3x+4(x+1)(x-1)3x+43x+43x+4(x+1)(x-1)(x+1)(x-1)(x+1)(x-1)•((x-1)2)/(x+2)-(2)/(x-1)•((x-1)2)/(x+2)
=((3x+4)(x-1))/((x-1)(x+2))-(2(x-1)2)/((x-1)(x+2))
=((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． ((x-1)2)/(x+2)(x-1)2x+2(x-1)2(x-1)2(x-1)22x+2x+2x+2-(2)/(x-1)•((x-1)2)/(x+2)
=((3x+4)(x-1))/((x-1)(x+2))-(2(x-1)2)/((x-1)(x+2))
=((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． (2)/(x-1)2x-1222x-1x-1x-1•((x-1)2)/(x+2)
=((3x+4)(x-1))/((x-1)(x+2))-(2(x-1)2)/((x-1)(x+2))
=((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． ((x-1)2)/(x+2)(x-1)2x+2(x-1)2(x-1)2(x-1)22x+2x+2x+2
=((3x+4)(x-1))/((x-1)(x+2))-(2(x-1)2)/((x-1)(x+2))
=((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． ((3x+4)(x-1))/((x-1)(x+2))(3x+4)(x-1)(x-1)(x+2)(3x+4)(x-1)(3x+4)(x-1)(3x+4)(x-1)(x-1)(x+2)(x-1)(x+2)(x-1)(x+2)-(2(x-1)2)/((x-1)(x+2))
=((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． (2(x-1)2)/((x-1)(x+2))2(x-1)2(x-1)(x+2)2(x-1)22(x-1)22(x-1)22(x-1)(x+2)(x-1)(x+2)(x-1)(x+2)
=((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． ((3x+4)(x-1)-2(x-1)2)/((x-1)(x+2))(3x+4)(x-1)-2(x-1)2(x-1)(x+2)(3x+4)(x-1)-2(x-1)2(3x+4)(x-1)-2(x-1)2(3x+4)(x-1)-2(x-1)22(x-1)(x+2)(x-1)(x+2)(x-1)(x+2)
=((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． ((x-1)[(3x+4)-2(x-1)])/((x-1)(x+2))(x-1)[(3x+4)-2(x-1)](x-1)(x+2)(x-1)[(3x+4)-2(x-1)](x-1)[(3x+4)-2(x-1)](x-1)[(3x+4)-2(x-1)](x-1)(x+2)(x-1)(x+2)(x-1)(x+2)
=(3x+4-2(x-1))/(x+2)
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． (3x+4-2(x-1))/(x+2)3x+4-2(x-1)x+23x+4-2(x-1)3x+4-2(x-1)3x+4-2(x-1)x+2x+2x+2
=(x+2)/(x+2)
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²-4）=8，
去括号，得x²+2x-x²-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解． (x+2)/(x+2)x+2x+2x+2x+2x+2x+2x+2x+2
=1；
（4）方程两边同时乘以（x+2）（x-2）得，x（x+2）-（x²2-4）=8，
去括号，得x²2+2x-x²2-4=8，
解得：x=6，
检验：当x=6时，（x+2）（x-2）=8×4=32≠0．
则x=6是方程的解．