Solve 14x-28/x^2-3x-4*x^2+9x+8divx-2

$$\frac{ 14x-28 }{ { x }^{ 2 } -3x-4 } \times { x }^{ 2 } +9x+8 \div x-2$$

Evaluate

$$\frac{23x^{4}-57x^{3}-22x^{2}-16x-32}{x\left(x-4\right)\left(x+1\right)}$$

Short Solution Steps

Express \frac{14x-28}{x^{2}-3x-4}x^{2} as a single fraction.

$$\frac{\left(14x-28\right)x^{2}}{x^{2}-3x-4}+9x+\frac{8}{x}-2$$

Factor x^{2}-3x-4.

$$\frac{\left(14x-28\right)x^{2}}{\left(x-4\right)\left(x+1\right)}+9x-2+\frac{8}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9x-2 times \frac{\left(x-4\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}.

$$\frac{\left(14x-28\right)x^{2}}{\left(x-4\right)\left(x+1\right)}+\frac{\left(9x-2\right)\left(x-4\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}+\frac{8}{x}$$

Since \frac{\left(14x-28\right)x^{2}}{\left(x-4\right)\left(x+1\right)} and \frac{\left(9x-2\right)\left(x-4\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(14x-28\right)x^{2}+\left(9x-2\right)\left(x-4\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}+\frac{8}{x}$$

Do the multiplications in \left(14x-28\right)x^{2}+\left(9x-2\right)\left(x-4\right)\left(x+1\right).

$$\frac{14x^{3}-28x^{2}+9x^{3}-27x^{2}-36x-2x^{2}+6x+8}{\left(x-4\right)\left(x+1\right)}+\frac{8}{x}$$

Combine like terms in 14x^{3}-28x^{2}+9x^{3}-27x^{2}-36x-2x^{2}+6x+8.

$$\frac{23x^{3}-57x^{2}-30x+8}{\left(x-4\right)\left(x+1\right)}+\frac{8}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-4\right)\left(x+1\right) and x is x\left(x-4\right)\left(x+1\right). Multiply \frac{23x^{3}-57x^{2}-30x+8}{\left(x-4\right)\left(x+1\right)} times \frac{x}{x}. Multiply \frac{8}{x} times \frac{\left(x-4\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}.

$$\frac{\left(23x^{3}-57x^{2}-30x+8\right)x}{x\left(x-4\right)\left(x+1\right)}+\frac{8\left(x-4\right)\left(x+1\right)}{x\left(x-4\right)\left(x+1\right)}$$

Since \frac{\left(23x^{3}-57x^{2}-30x+8\right)x}{x\left(x-4\right)\left(x+1\right)} and \frac{8\left(x-4\right)\left(x+1\right)}{x\left(x-4\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(23x^{3}-57x^{2}-30x+8\right)x+8\left(x-4\right)\left(x+1\right)}{x\left(x-4\right)\left(x+1\right)}$$

Do the multiplications in \left(23x^{3}-57x^{2}-30x+8\right)x+8\left(x-4\right)\left(x+1\right).

$$\frac{23x^{4}-57x^{3}-30x^{2}+8x+8x^{2}+8x-32x-32}{x\left(x-4\right)\left(x+1\right)}$$

Combine like terms in 23x^{4}-57x^{3}-30x^{2}+8x+8x^{2}+8x-32x-32.

$$\frac{23x^{4}-57x^{3}-22x^{2}-16x-32}{x\left(x-4\right)\left(x+1\right)}$$

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

$$\frac{23x^{4}-57x^{3}-22x^{2}-16x-32}{x^{3}-3x^{2}-4x}$$

Expand

$$\frac{23x^{4}-57x^{3}-22x^{2}-16x-32}{x\left(x^{2}-3x-4\right)}$$

Short Solution Steps

Express \frac{14x-28}{x^{2}-3x-4}x^{2} as a single fraction.

$$\frac{\left(14x-28\right)x^{2}}{x^{2}-3x-4}+9x+\frac{8}{x}-2$$

Factor x^{2}-3x-4.

$$\frac{\left(14x-28\right)x^{2}}{\left(x-4\right)\left(x+1\right)}+9x-2+\frac{8}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9x-2 times \frac{\left(x-4\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}.

$$\frac{\left(14x-28\right)x^{2}}{\left(x-4\right)\left(x+1\right)}+\frac{\left(9x-2\right)\left(x-4\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}+\frac{8}{x}$$

Since \frac{\left(14x-28\right)x^{2}}{\left(x-4\right)\left(x+1\right)} and \frac{\left(9x-2\right)\left(x-4\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(14x-28\right)x^{2}+\left(9x-2\right)\left(x-4\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}+\frac{8}{x}$$

Do the multiplications in \left(14x-28\right)x^{2}+\left(9x-2\right)\left(x-4\right)\left(x+1\right).

$$\frac{14x^{3}-28x^{2}+9x^{3}-27x^{2}-36x-2x^{2}+6x+8}{\left(x-4\right)\left(x+1\right)}+\frac{8}{x}$$

Combine like terms in 14x^{3}-28x^{2}+9x^{3}-27x^{2}-36x-2x^{2}+6x+8.

$$\frac{23x^{3}-57x^{2}-30x+8}{\left(x-4\right)\left(x+1\right)}+\frac{8}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-4\right)\left(x+1\right) and x is x\left(x-4\right)\left(x+1\right). Multiply \frac{23x^{3}-57x^{2}-30x+8}{\left(x-4\right)\left(x+1\right)} times \frac{x}{x}. Multiply \frac{8}{x} times \frac{\left(x-4\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}.

$$\frac{\left(23x^{3}-57x^{2}-30x+8\right)x}{x\left(x-4\right)\left(x+1\right)}+\frac{8\left(x-4\right)\left(x+1\right)}{x\left(x-4\right)\left(x+1\right)}$$

Since \frac{\left(23x^{3}-57x^{2}-30x+8\right)x}{x\left(x-4\right)\left(x+1\right)} and \frac{8\left(x-4\right)\left(x+1\right)}{x\left(x-4\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(23x^{3}-57x^{2}-30x+8\right)x+8\left(x-4\right)\left(x+1\right)}{x\left(x-4\right)\left(x+1\right)}$$

Do the multiplications in \left(23x^{3}-57x^{2}-30x+8\right)x+8\left(x-4\right)\left(x+1\right).

$$\frac{23x^{4}-57x^{3}-30x^{2}+8x+8x^{2}+8x-32x-32}{x\left(x-4\right)\left(x+1\right)}$$

Combine like terms in 23x^{4}-57x^{3}-30x^{2}+8x+8x^{2}+8x-32x-32.

$$\frac{23x^{4}-57x^{3}-22x^{2}-16x-32}{x\left(x-4\right)\left(x+1\right)}$$

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

$$\frac{23x^{4}-57x^{3}-22x^{2}-16x-32}{x^{3}-3x^{2}-4x}$$