Solve 11/m^2-1-1/1-m^2

$$\frac { 11 } { m ^ { 2 } - 1 } - \frac { 1 } { 1 - m ^ { 2 } }$$

Evaluate

$$\frac{12}{m^{2}-1}$$

Short Solution Steps

Factor m^{2}-1. Factor 1-m^{2}.

$$\frac{11}{\left(m-1\right)\left(m+1\right)}-\frac{1}{\left(m-1\right)\left(-m-1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-1\right)\left(m+1\right) and \left(m-1\right)\left(-m-1\right) is \left(m-1\right)\left(m+1\right). Multiply \frac{1}{\left(m-1\right)\left(-m-1\right)} times \frac{-1}{-1}.

$$\frac{11}{\left(m-1\right)\left(m+1\right)}-\frac{-1}{\left(m-1\right)\left(m+1\right)}$$

Since \frac{11}{\left(m-1\right)\left(m+1\right)} and \frac{-1}{\left(m-1\right)\left(m+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-\left(-1\right)}{\left(m-1\right)\left(m+1\right)}$$

Do the multiplications in 11-\left(-1\right).

$$\frac{11+1}{\left(m-1\right)\left(m+1\right)}$$

Do the calculations in 11+1.

$$\frac{12}{\left(m-1\right)\left(m+1\right)}$$

Expand \left(m-1\right)\left(m+1\right).

$$\frac{12}{m^{2}-1}$$

Differentiate w.r.t. m

$$-\frac{24m}{\left(m^{2}-1\right)^{2}}$$