Solve 2x/5x^2-1c-x/x-2

$$\frac{ 2x }{ 5 { x }^{ 2 } -1c } - \frac{ x }{ x-2 }$$

Evaluate

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

Short Solution Steps

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

$$\frac{2x\left(x-2\right)}{\left(x-2\right)\left(5x^{2}-c\right)}-\frac{x\left(5x^{2}-c\right)}{\left(x-2\right)\left(5x^{2}-c\right)}$$

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

$$\frac{2x\left(x-2\right)-x\left(5x^{2}-c\right)}{\left(x-2\right)\left(5x^{2}-c\right)}$$

Do the multiplications in 2x\left(x-2\right)-x\left(5x^{2}-c\right).

$$\frac{2x^{2}-4x-5x^{3}+xc}{\left(x-2\right)\left(5x^{2}-c\right)}$$

Expand \left(x-2\right)\left(5x^{2}-c\right).

$$\frac{2x^{2}-4x-5x^{3}+xc}{5x^{3}-10x^{2}-cx+2c}$$

Factor

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