Solve 3x+9/x-4*4x-16

$$\frac{ 3x+9 }{ x-4 } \times 4x-16$$

Evaluate

$$\frac{4\left(3x^{2}+5x+16\right)}{x-4}$$

Short Solution Steps

Express \frac{3x+9}{x-4}\times 4 as a single fraction.

$$\frac{\left(3x+9\right)\times 4}{x-4}x-16$$

Express \frac{\left(3x+9\right)\times 4}{x-4}x as a single fraction.

$$\frac{\left(3x+9\right)\times 4x}{x-4}-16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{x-4}{x-4}.

$$\frac{\left(3x+9\right)\times 4x}{x-4}-\frac{16\left(x-4\right)}{x-4}$$

Since \frac{\left(3x+9\right)\times 4x}{x-4} and \frac{16\left(x-4\right)}{x-4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(3x+9\right)\times 4x-16\left(x-4\right)}{x-4}$$

Do the multiplications in \left(3x+9\right)\times 4x-16\left(x-4\right).

$$\frac{12x^{2}+36x-16x+64}{x-4}$$

Combine like terms in 12x^{2}+36x-16x+64.

$$\frac{12x^{2}+20x+64}{x-4}$$

Expand

$$\frac{4\left(3x^{2}+5x+16\right)}{x-4}$$

Short Solution Steps

Express \frac{3x+9}{x-4}\times 4 as a single fraction.

$$\frac{\left(3x+9\right)\times 4}{x-4}x-16$$

Express \frac{\left(3x+9\right)\times 4}{x-4}x as a single fraction.

$$\frac{\left(3x+9\right)\times 4x}{x-4}-16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{x-4}{x-4}.

$$\frac{\left(3x+9\right)\times 4x}{x-4}-\frac{16\left(x-4\right)}{x-4}$$

Since \frac{\left(3x+9\right)\times 4x}{x-4} and \frac{16\left(x-4\right)}{x-4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(3x+9\right)\times 4x-16\left(x-4\right)}{x-4}$$

Do the multiplications in \left(3x+9\right)\times 4x-16\left(x-4\right).

$$\frac{12x^{2}+36x-16x+64}{x-4}$$

Combine like terms in 12x^{2}+36x-16x+64.

$$\frac{12x^{2}+20x+64}{x-4}$$