Solve m/m+1+5/m-1=1

$$\frac { m } { m + 1 } + \frac { 5 } { m - 1 } = 1$$

Solve for m

$$m = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

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.

$$\left(m-1\right)m+\left(m+1\right)\times 5=\left(m-1\right)\left(m+1\right)$$

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

$$m^{2}-m+\left(m+1\right)\times 5=\left(m-1\right)\left(m+1\right)$$

Use the distributive property to multiply m+1 by 5.

$$m^{2}-m+5m+5=\left(m-1\right)\left(m+1\right)$$

Combine -m and 5m to get 4m.

$$m^{2}+4m+5=\left(m-1\right)\left(m+1\right)$$

Consider \left(m-1\right)\left(m+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$m^{2}+4m+5=m^{2}-1$$

Subtract m^{2} from both sides.

$$m^{2}+4m+5-m^{2}=-1$$

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

$$4m+5=-1$$

Subtract 5 from both sides.

$$4m=-1-5$$

Subtract 5 from -1 to get -6.

$$4m=-6$$

Divide both sides by 4.

$$m=\frac{-6}{4}$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$m=-\frac{3}{2}$$