Question

解方程1/x-1+1/x+3=4/x^2-9

Answer 1

(x+3)(x-3)+(x-3)(x-1)=4(x-1)

(x-3)[(x+3)+(x-1)]=4x-4

(x-3)(2x+2)=4x-4

2x^2+2x-6x-6=4x-4

2x^2+2x-4x-6x=2

2^2+8x=2

x^2+4x=1

x^2+4x+4=1

x^2+4x+2^2=5

(x-2)^2=5

x-2=±√5

x1=2+√5

x2=2-√5

最后记得验根

所以

x=2±√5为方程旳解