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

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

Evaluate

$$\frac{25-10x-13x^{2}}{x\left(5-4x\right)}$$

Short Solution Steps

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

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

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

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

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

$$\frac{-20x+25-5x^{2}}{x\left(-4x+5\right)}+2$$

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

$$\frac{-20x+25-5x^{2}}{x\left(-4x+5\right)}+\frac{2x\left(-4x+5\right)}{x\left(-4x+5\right)}$$

Since \frac{-20x+25-5x^{2}}{x\left(-4x+5\right)} and \frac{2x\left(-4x+5\right)}{x\left(-4x+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{-20x+25-5x^{2}+2x\left(-4x+5\right)}{x\left(-4x+5\right)}$$

Do the multiplications in -20x+25-5x^{2}+2x\left(-4x+5\right).

$$\frac{-20x+25-5x^{2}-8x^{2}+10x}{x\left(-4x+5\right)}$$

Combine like terms in -20x+25-5x^{2}-8x^{2}+10x.

$$\frac{-10x+25-13x^{2}}{x\left(-4x+5\right)}$$

Expand x\left(-4x+5\right).

$$\frac{-10x+25-13x^{2}}{-4x^{2}+5x}$$

Differentiate w.r.t. x

$$\frac{5\left(-21x^{2}+40x-25\right)}{\left(x\left(4x-5\right)\right)^{2}}$$