Solve 5x-4/x-2*3x-6

$$\frac { 5 x - 4 } { x - 2 } \times 3 x - 6$$

Evaluate

$$\frac{3\left(5x^{2}-6x+4\right)}{x-2}$$

Short Solution Steps

Express \frac{5x-4}{x-2}\times 3 as a single fraction.

$$\frac{\left(5x-4\right)\times 3}{x-2}x-6$$

Express \frac{\left(5x-4\right)\times 3}{x-2}x as a single fraction.

$$\frac{\left(5x-4\right)\times 3x}{x-2}-6$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{x-2}{x-2}.

$$\frac{\left(5x-4\right)\times 3x}{x-2}-\frac{6\left(x-2\right)}{x-2}$$

Since \frac{\left(5x-4\right)\times 3x}{x-2} and \frac{6\left(x-2\right)}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(5x-4\right)\times 3x-6\left(x-2\right)}{x-2}$$

Do the multiplications in \left(5x-4\right)\times 3x-6\left(x-2\right).

$$\frac{15x^{2}-12x-6x+12}{x-2}$$

Combine like terms in 15x^{2}-12x-6x+12.

$$\frac{15x^{2}-18x+12}{x-2}$$

Expand

$$\frac{3\left(5x^{2}-6x+4\right)}{x-2}$$

Short Solution Steps

Express \frac{5x-4}{x-2}\times 3 as a single fraction.

$$\frac{\left(5x-4\right)\times 3}{x-2}x-6$$

Express \frac{\left(5x-4\right)\times 3}{x-2}x as a single fraction.

$$\frac{\left(5x-4\right)\times 3x}{x-2}-6$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{x-2}{x-2}.

$$\frac{\left(5x-4\right)\times 3x}{x-2}-\frac{6\left(x-2\right)}{x-2}$$

Since \frac{\left(5x-4\right)\times 3x}{x-2} and \frac{6\left(x-2\right)}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(5x-4\right)\times 3x-6\left(x-2\right)}{x-2}$$

Do the multiplications in \left(5x-4\right)\times 3x-6\left(x-2\right).

$$\frac{15x^{2}-12x-6x+12}{x-2}$$

Combine like terms in 15x^{2}-12x-6x+12.

$$\frac{15x^{2}-18x+12}{x-2}$$