AHSME 1952 Problem 23

If $\frac{x^2-bx}{ax-c}=\frac{m-1}{m+1}$ has roots which are numerically equal but of opposite signs, the value of $m$ must be: $\textbf{(A) \ }\frac{a-b}{a+b} \textbf{(B) \ }\frac{a+b}{a-b} \textbf{(C) \ }c \textbf{(D) \ }\frac{1}{c} \textbf{(E) \ }1$