x为(根号2)减1的倒数,《（x减3）分之（x方减x减6）》除以《（x方加x减6)分之（x加3）》的值

要过程、谢谢、

x=1/(根号2-1)=根号2+1

[(x^2-x-6)/(x-3)]/[(x^2+x-6)/(x+3)]=[(x+2)(x-3)/(x-3)]/[(x-2)(x+3)/(x+3)]=(x+2)/(x-2)=1+4/(x-2)=1+4/(根号2-1）

=1+4(根号2+1)=5+4 根号2

1.。x=1/√ 2-1=√ 2+1/(√ 2-1)(√ 2+1)=√ 2+1/2-1=√ 2+1

x^2-x+6/x-3 处以x+3/x^2+x+6

得(x+2)(x-3)/(x-3) 处以 x+3/(x-2)(x+3)

得x+2/x-2

把x=√ 2+1带入上式

得√ 2+1+2/√ 2+1-2=√ 2+3/√ 2-1=（√ 2+3）（√ 2+1)/(√ 2+1)(√ 2-1)=(√ 2+3）（√ 2+1）=4+4√ 2+3=7+4√ 2

x方减x减6=(x-3)(x+2)

（x减3）分之（x方减x减6）=(x+2)

x方加x减6=(x+3)(x-2)

（x方加x减6)分之（x加3）=1/(x-2)

《（x减3）分之（x方减x减6）》除以《（x方加x减6)分之（x加3）》= (x+2)(x-2) = x平方-4 = 2倍根号2 -1

∵x=1/（√2-1）=√2+1

∴[（x²-x-6）/（x-3）]÷[（x+3）/（x²+x-6）]=[(x-3)(x+2)/(x-3)]×[(x+3)(x-2)/(x+3)]

=(x+2)/(x-2)

=(√2+3)/(√2-1)

=(√2+3)(√2+1)

=5+4 √2

解：

x=1/(√2-1)

=(√2+1)/[(√2-1)(√2+1)]

=(√2+1)/[2-1]

=√2+1

原式

=[(x^2-x-6)/(x-3)]/[(x+3)/(x^2+x-6)]

=[(x+2)(x-3)/(x-3)]/[(x+3)/(x+3)(x-2)]

=[(x+2)]/[1/(x-2)]

=(x+2)(x-2)

=x^2-2^2

=(√2+1)^2-2^2

=(3+2√2)-4

=2√2-1

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