計算(x的平方-x-6)÷(x-3)

計算(x的平方-x-6)÷(x-3)

(x的平方-x-6)÷(x-3)
=(x+2)(x-3)÷(x-3)
=x+2

計算(2x-6)/x的平方-4x+4÷(x+3)×(x的平方+x-6)/(3-x) (x+3)和(x的平方+x-6)是兩個式子!

原式=2(x-3)/[(x-2)^2]*1/(x+3)*(x+3)(x-2)/(3-x)
=-2/(x-2)

計算x-5分之1-x的平方-25分之6-10+2x分之x+1

=1/(x-5)-6/(x+5)(x-5)-(x+1)/2(x+5)
=2(x+5)/2(x+5)(x-5)-12/2(x+5)(x-5)-(x+1)(x-5)/2(x+5)(x-5)
=(2x+10-12-x²+4x+5)/2(x²-25)
=(-x²+6x+3)/(2x²-50)
=-(x²-6x-3)/(2x²-50)

計算1+1+2分之1++1+2+3分之1+1+2+3+…+100分之1 =

利用等差數列求和公式,知
1+2+3+4+.+n=(1+n)*N/2
所以原式可化為1+2*(1/(2*3)+1/(3*4)+.+1/(100*101))
由裂項法1/(n(n+1))=(1/n)-(1/(n+1))
可得
=1+2*(1/2-1/101)
=200/101

x^2-4分之2x-2-x分之1+x+2分之3計算

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

1.計算①(x-1-x+1分之8)×x+3分之x+1; ②x+3y分之x-y÷x²+6xy+9y²分之x²-y²-x+y分之2y;③(x-x+1分之2x)÷x²-1分之x²-2x+1 ④(x²-2x分之x+2-x²-4x+4分之x-1)÷x³-2x²分之x-4

①(x-1-x+1分之8)×x+3分之x+1;
=(x²-1-8)/(x+1)×(x+1)/(x+3)
=x-3;
②x+3y分之x-y÷x²+6xy+9y²分之x²-y²-x+y分之2y;
=(x-y)/(x+3y)×(x+3y)²/(x+y)(x-y)-2y/(x+y)
=(x+3y)/(x+y)-2y/(x+y)
=1;
③(x-x+1分之2x)÷x²-1分之x²-2x+1
=(x²+x-2x)/(x+1)×(x+1)(x-1)/(x-1)²
=x(x-1)/(x-1)
=x;
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