Solve 1/2m-1-1/2m^2-2m+1

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2m-1 and 2m^{2}-2m+1 is \left(2m-1\right)\left(2m^{2}-2m+1\right). Multiply \frac{1}{2m-1} times \frac{2m^{2}-2m+1}{2m^{2}-2m+1}. Multiply \frac{1}{2m^{2}-2m+1} times \frac{2m-1}{2m-1}.

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

Since \frac{2m^{2}-2m+1}{\left(2m-1\right)\left(2m^{2}-2m+1\right)} and \frac{2m-1}{\left(2m-1\right)\left(2m^{2}-2m+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2m^{2}-2m+1-\left(2m-1\right).

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

Combine like terms in 2m^{2}-2m+1-2m+1.

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

Expand \left(2m-1\right)\left(2m^{2}-2m+1\right).

$$\frac{2m^{2}-4m+2}{4m^{3}-6m^{2}+4m-1}$$

Differentiate w.r.t. m

$$\frac{4\left(m-1\right)\left(1-4m+6m^{2}-2m^{3}\right)}{\left(2m-1\right)^{2}\left(4m^{4}-8m^{3}+8m^{2}-4m+1\right)}$$