Question

x/ x-2 + x-1 / x+1 = -1

I need help working it out!

Answer 1

\[\frac{ x }{ x-2 }-\frac{ x-1 }{ x+1 }=-1,x \neq2,x \neq -1\]
\[\frac{ x }{ x-2 }=-1+\frac{ x-1 }{ x+1 }=\frac{ -x-1+x-1 }{ x+1 }=\frac{ -2 }{ x+1 }\]
\[x(x+1)=-2(x-2),x^2+x+2(x-2)=0,x^2+3x-4=0\]
\[x^2+4x-x-4=0,x(x+4)-1(x+4)=0,(x+4)(x-1)=0,x=-4,x=1\]