Solve m-1/m+1-2m/m-1=-1

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

Solve for m

$$m=0$$

Steps for Solving Linear Equation

Variable m cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(m-1\right)\left(m+1\right), the least common multiple of m+1,m-1.

$$\left(m-1\right)\left(m-1\right)-\left(m+1\right)\times 2m=-\left(m-1\right)\left(m+1\right)$$

Multiply m-1 and m-1 to get \left(m-1\right)^{2}.

$$\left(m-1\right)^{2}-\left(m+1\right)\times 2m=-\left(m-1\right)\left(m+1\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m-1\right)^{2}.

$$m^{2}-2m+1-\left(m+1\right)\times 2m=-\left(m-1\right)\left(m+1\right)$$

Use the distributive property to multiply m+1 by 2.

$$m^{2}-2m+1-\left(2m+2\right)m=-\left(m-1\right)\left(m+1\right)$$

Use the distributive property to multiply 2m+2 by m.

$$m^{2}-2m+1-\left(2m^{2}+2m\right)=-\left(m-1\right)\left(m+1\right)$$

To find the opposite of 2m^{2}+2m, find the opposite of each term.

$$m^{2}-2m+1-2m^{2}-2m=-\left(m-1\right)\left(m+1\right)$$

Combine m^{2} and -2m^{2} to get -m^{2}.

$$-m^{2}-2m+1-2m=-\left(m-1\right)\left(m+1\right)$$

Combine -2m and -2m to get -4m.

$$-m^{2}-4m+1=-\left(m-1\right)\left(m+1\right)$$

Use the distributive property to multiply -1 by m-1.

$$-m^{2}-4m+1=\left(-m+1\right)\left(m+1\right)$$

Use the distributive property to multiply -m+1 by m+1 and combine like terms.

$$-m^{2}-4m+1=-m^{2}+1$$

Add m^{2} to both sides.

$$-m^{2}-4m+1+m^{2}=1$$

Combine -m^{2} and m^{2} to get 0.

$$-4m+1=1$$

Subtract 1 from both sides.

$$-4m=1-1$$

Subtract 1 from 1 to get 0.

$$-4m=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -4 is not equal to 0, m must be equal to 0.

$$m=0$$