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

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

Solve for m

$$m=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$m=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Steps by Finding Square Root

Variable m cannot be equal to any of the values -1,-\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(m+1\right)\left(2m+1\right), the least common multiple of 2m+1,1+m.

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

Use the distributive property to multiply m+1 by 2m-1 and combine like terms.

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

Use the distributive property to multiply 2m+1 by 1-m and combine like terms.

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

Subtract m from both sides.

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

Combine m and -m to get 0.

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

Add 2m^{2} to both sides.

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

Combine 2m^{2} and 2m^{2} to get 4m^{2}.

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

Add 1 to both sides.

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

Add 1 and 1 to get 2.

$$4m^{2}=2$$

Divide both sides by 4.

$$m^{2}=\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$m^{2}=\frac{1}{2}$$

Take the square root of both sides of the equation.

$$m=\frac{\sqrt{2}}{2} m=-\frac{\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Variable m cannot be equal to any of the values -1,-\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(m+1\right)\left(2m+1\right), the least common multiple of 2m+1,1+m.

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

Use the distributive property to multiply m+1 by 2m-1 and combine like terms.

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

Use the distributive property to multiply 2m+1 by 1-m and combine like terms.

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

Subtract m from both sides.

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

Combine m and -m to get 0.

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

Add 2m^{2} to both sides.

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

Combine 2m^{2} and 2m^{2} to get 4m^{2}.

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

Subtract 1 from both sides.

$$4m^{2}-1-1=0$$

Subtract 1 from -1 to get -2.

$$4m^{2}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 4\left(-2\right)}}{2\times 4}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 4\left(-2\right)}}{2\times 4}$$

Multiply -4 times 4.

$$m=\frac{0±\sqrt{-16\left(-2\right)}}{2\times 4}$$

Multiply -16 times -2.

$$m=\frac{0±\sqrt{32}}{2\times 4}$$

Take the square root of 32.

$$m=\frac{0±4\sqrt{2}}{2\times 4}$$

Multiply 2 times 4.

$$m=\frac{0±4\sqrt{2}}{8}$$

Now solve the equation m=\frac{0±4\sqrt{2}}{8} when ± is plus.

$$m=\frac{\sqrt{2}}{2}$$

Now solve the equation m=\frac{0±4\sqrt{2}}{8} when ± is minus.

$$m=-\frac{\sqrt{2}}{2}$$

The equation is now solved.

$$m=\frac{\sqrt{2}}{2} m=-\frac{\sqrt{2}}{2}$$