Question

奥数计算题

1.(x^3-x^2-4x+1)/(x^2-3x+2)-(x^3-2x^2-9x+21)/（x^2-5x+6）+（x^2-3x+8）/（x^2-4x+3）
2.{(x^2)/（x-y)}*{y/(x+y)}-{(x^4y)/(x^4-y^4)}÷{（x^2/x^2+y^2）^2}

Answer 1

1.(x³-x²-4x+1)/(x²-3x+2)-(x³-2x²-9x+21)/（x²-5x+6）+（x²-3x+8）/（x²-4x+3）
=.(x³-x²-4x+1)/(x-1)(x-2)-(x³-2x²-9x+21)/(x-2)(x-3)+(x²-3x+8)/(x-1)(x-3)
=[(x³-x²-4x+1)(x-3)-(x³-2x²-9x+21)(x-1)+(x²-3x+8)(x-2)]/(x-1)(x-2)(x-3)
=[(x⁴-4x³-x²+13x-3)-(x⁴-3x³-7x²+30x-21)+(x³-5x²+14x-16)]/(x-1)(x-2)(x-3)
=(x²-3x+2)/(x-1)(x-2)(x-3)=(x-1)(x-2)/(x-1)(x-2)(x-3)=1/(x-3)
2.{x²/（x-y)}*{y/(x+y)}-{(x⁴y)/(x⁴-y⁴)}÷{[x²/(x²+y²)]²}
=x²y/(x²-y²)-[x⁴y/(x²+y²)(x²-y²)][(x²+y²)/x²]²
=x²y/(x²-y²)-y(x²+y²)/(x²-y²)=[x²y-y(x²+y²)]/(x²-y²)=-y³/(x²-y²)