Question

分式加减

Answer 1

1/(1-x)+1/(1+x)+2/(1+x²)
=(1+x+1-x)/(1-x²)+2/(1+x²)
=(2+2x²+2-2x²)/(1-x^4)
=4/(1-x^4)

2/(x-1)-2/(x+1)-1/(x-2)+1/(x+2)
=(2x+2-2x+2)/(x²-1)-(x+2+x-2)/(x²-4)
=4/(x²-1)-2x/(x²-4)
=(4x²-16-2x³+2x)/(x²-1)(x²-4)

(ab+b²)÷(a²-b²)/(a-b)
=b(a+b)×(a-b)/(a-b)(a+b)
=b

3x/(x-4y)+(x+y)/(4y-x)-7y/(x-4y)
=3x/(x-4y)-(x+y)/(x-4y)-7y/(x-4y)
=(3x-x-y-7y)/(x-4y)
=2(x-4y)/(x-4y)
=2