Solve 4/2x+1-2/5x-1

$$\frac { 4 } { 2 x + 1 } - \frac { 2 } { 5 x - 1 }$$

Evaluate

$$\frac{2\left(8x-3\right)}{\left(5x-1\right)\left(2x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x+1 and 5x-1 is \left(5x-1\right)\left(2x+1\right). Multiply \frac{4}{2x+1} times \frac{5x-1}{5x-1}. Multiply \frac{2}{5x-1} times \frac{2x+1}{2x+1}.

$$\frac{4\left(5x-1\right)}{\left(5x-1\right)\left(2x+1\right)}-\frac{2\left(2x+1\right)}{\left(5x-1\right)\left(2x+1\right)}$$

Since \frac{4\left(5x-1\right)}{\left(5x-1\right)\left(2x+1\right)} and \frac{2\left(2x+1\right)}{\left(5x-1\right)\left(2x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(5x-1\right)-2\left(2x+1\right)}{\left(5x-1\right)\left(2x+1\right)}$$

Do the multiplications in 4\left(5x-1\right)-2\left(2x+1\right).

$$\frac{20x-4-4x-2}{\left(5x-1\right)\left(2x+1\right)}$$

Combine like terms in 20x-4-4x-2.

$$\frac{16x-6}{\left(5x-1\right)\left(2x+1\right)}$$

Expand \left(5x-1\right)\left(2x+1\right).

$$\frac{16x-6}{10x^{2}+3x-1}$$

Factor

$$\frac{2\left(8x-3\right)}{\left(5x-1\right)\left(2x+1\right)}$$