If a^2-3a+1=0 , find the value of the algebraic expression 3a^3-8a^2+a+\dfrac{3}{a^2+1}

Given a+b+c=0 , abc ≠ 0 , a, b,c, are not equal to each other, find the value of

\dfrac{a^2}{bc} +\dfrac{b^2}{ac} +\dfrac{c^2}{ab}

If a, b, c are rational numbers but not zero, a+b+c=0 , what is the value of

\dfrac{1}{b^2+c^2-a^2} +\dfrac{1}{c^2+a^2-b^2} +\dfrac{1}{a^2+b^2-c^2}

If real numbers a,b, c satisfy a+b+c=0 , abc=4 , which one best describes the value of

\dfrac{1}{a} +\dfrac{1}{b} +\dfrac{1}{c}

If a+b+c=0 , \dfrac{b-c}{a}+\dfrac{c-a}{b}+\dfrac{a-b}{c}=0 , prove \dfrac{bc+b-c}{b^2c^2}+\dfrac{ca+c-a}{c^2a^2}+\dfrac{ab+a-b}{a^2b^2}=0

If 2x+y=0 , which one is correct for the value of the fractional expression \dfrac{x^2+xy+y^2}{2xy-x^2}

\dfrac{ 2007²}{(2007＋1)×(2007－1) ＋1}

Simplify \dfrac{a^2-b^2}{ab}-\dfrac{ab-b^2}{ab-a^2} , its result is

Simplify the algebraic expression (\dfrac{a^2}{a-3}+\dfrac{9}{3-a})÷\dfrac{a+3}{a} , it’s result is

For any natural number n , the fraction \dfrac{21n+4}{14n+3} cannot be reduced

If abc=1 , prove \dfrac{a}{1+a+ab}+\dfrac{b}{1+b+bc}+\dfrac{c}{1+c+ca} =1

If \dfrac{1}{x}-\dfrac{1}{y}=3 , find the value of \dfrac{2x+3xy-2y}{x-2xy-y}