Question

4x/(x2+x+3)+5x(x2-5x+3)=-3/2,要求简便方法de完整过程

Answer 1

当X=0 左边=0

当X0 X^2-5X+3>0 左边0

设X+3/X=T>=2√3

左边两个分式的分子分母同除X

4X/(X^2+X+3)=4/(X+3/X+1)=4/(T+1)

5X/(X^2-5X+3)=5/(X+3/X-5)=5/(T-5)

得到

4/(T+1)+5/(T-5)=3/2 左右同乘2(T+1)(T-5)

8(T-5)+10(T+1)=3(T+1)(T-5)

3T^2-30T+15=0

T^2-10T+5=0

T=5+2√5或5-2√5

5-2√5