Solve 1/3n-5-1/3n-2=

$$\frac { 1 } { 3 n - 5 } - \frac { 1 } { 3 n - 2 } =$$

Evaluate

$$\frac{3}{\left(3n-5\right)\left(3n-2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3n-5 and 3n-2 is \left(3n-5\right)\left(3n-2\right). Multiply \frac{1}{3n-5} times \frac{3n-2}{3n-2}. Multiply \frac{1}{3n-2} times \frac{3n-5}{3n-5}.

$$\frac{3n-2}{\left(3n-5\right)\left(3n-2\right)}-\frac{3n-5}{\left(3n-5\right)\left(3n-2\right)}$$

Since \frac{3n-2}{\left(3n-5\right)\left(3n-2\right)} and \frac{3n-5}{\left(3n-5\right)\left(3n-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3n-2-\left(3n-5\right)}{\left(3n-5\right)\left(3n-2\right)}$$

Do the multiplications in 3n-2-\left(3n-5\right).

$$\frac{3n-2-3n+5}{\left(3n-5\right)\left(3n-2\right)}$$

Combine like terms in 3n-2-3n+5.

$$\frac{3}{\left(3n-5\right)\left(3n-2\right)}$$

Expand \left(3n-5\right)\left(3n-2\right).

$$\frac{3}{9n^{2}-21n+10}$$

Differentiate w.r.t. n

$$\frac{9\left(7-6n\right)}{\left(\left(3n-5\right)\left(3n-2\right)\right)^{2}}$$