Question

In the equation $\frac{x(x-1)-(m+1)}{(x-1)(m-1)}=\frac{x}{m}$, the roots are equal when m = ______.

• A. $\frac{1}{2}$
• B. $-\frac{1}{2}$
• C. $0$
• D. $1$

Answer 1

Answer: (B)

$-\frac{1}{2}$

$\frac{x(x-1)-(m+1)}{(x-1)(m-1)}=\frac{x}{m}$

$m{x}^2-mx-m^2-m=x^{2}m-mx-x^2+x$

$x^2-x-m(m+1)=0$

Roots are equal

$△=0$

$1+4(m^2+m)=0$

$4m^2+4m+1=0$

$(2m+1{)}^2=0$

$\therefore m=-\frac{1}{2}$