Solve 6/x-1-5x/4

$$\frac{ 6 }{ x-1 } - \frac{ 5x }{ 4 }$$

Evaluate

$$\frac{24+5x-5x^{2}}{4\left(x-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and 4 is 4\left(x-1\right). Multiply \frac{6}{x-1} times \frac{4}{4}. Multiply \frac{5x}{4} times \frac{x-1}{x-1}.

$$\frac{6\times 4}{4\left(x-1\right)}-\frac{5x\left(x-1\right)}{4\left(x-1\right)}$$

Since \frac{6\times 4}{4\left(x-1\right)} and \frac{5x\left(x-1\right)}{4\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\times 4-5x\left(x-1\right)}{4\left(x-1\right)}$$

Do the multiplications in 6\times 4-5x\left(x-1\right).

$$\frac{24-5x^{2}+5x}{4\left(x-1\right)}$$

Expand 4\left(x-1\right).

$$\frac{24-5x^{2}+5x}{4x-4}$$

Factor

$$-\frac{\frac{5}{4}\left(x-\left(-\frac{\sqrt{505}}{10}+\frac{1}{2}\right)\right)\left(x-\left(\frac{\sqrt{505}}{10}+\frac{1}{2}\right)\right)}{x-1}$$