Question

因式分解还有几道计算题，求过程

（1）64a四次方-1 （2）3X三次方-12X²y+12xy² （3）（根号2-1）零次方-2²+（2/3）-² （4）12/m²-9+1/3-m+2/m+3 （5）5/x-1=3/x+1 （6）4/x²-2x+1/x=2/x-2 先化简：x²-1/x²+2x+1÷x-1/x+1-x/x+1。最对x去一个你喜欢的数代入求值

Answer 1

(1)
=（8a^2-1)(8a^2+1)
(2)
=3x(x²-4xy+4y²)=3x(x-2y)^2
(3)
=1-4+9/4=-3/4
(4)
12/(m^2-9)+2/(3-m)+2/(m+3)
=12/(m+3)(m-3)-2(m+3)/(m+3)(m-3)+2(m-3)/(m+3)(m-3)
=[12-2(m+3)+2(m-3)]/(m+3)(m-3)
=(12-2m-6+2m-6)/(m+3)(m-3)
=0
(5)
5/(x-1)=3/(x+1)
5(x+1)=3(x-1)
5x+5=3x-3
2x=-8
x=-4
(6)
4/(x²-2x)+1/x=2/(x-2)
4+x-2=2x
x=2

(x²-1)/(x²+2x+1)/(x-1)/(x+1)-x/(x+1)
=(x+1)(x-1)/(x+1)²*(x+1)/(x-1)-x/(x+1)
=(x-1)/(x+1)×(x+1)/(x-1)-x/(x+1)
=1 - x/(x+1)
=(x+1-x)/(x+1)
=1/(x+1)
x=2时，原式=1/(2+1)=1/3

Answer 2

 

Answer 3

(1)64a^4-1=(8a²+1)(8a²-1)
(2)3x³-12x²y+12xy²=3x(x²-4xy+4y²)=3x(x-2y)²
(3)(√2-1)^0-2²+(2/3)^(-2)=1-4+9/4=-3/4
(4)12/(m²-9)+1/(3-m)+2/(m+3)
=[12-(m+3)+2(m-3)]/(m²-9)
=(m+3)/[(m+3)(m-3)]
=1/(m-3)
(5)5/(x-1)=3/(x+1)
5(x+1)=3(x-1)
5x+5=3x-3
2x=-8
x=-4
(6)4/(x²-2x)+1/x=2/(x-2)
4+x-2=2x
x=2
(7)(x²-1)/(x²+2x+1)÷(x-1)/(x+1)-x/(x+1)
=(x+1)(x-1)/(x+1)²×(x+1)/(x-1)-x/(x+1)
=(x-1)/(x+1)×(x+1)/(x-1)-x/(x+1)
=1-x/(x+1)
=(x+1-x)/(x+1)
=1/(x+1)
取x=2，那么原式=1/(2+1)=1/3