Solve x^3+3/x^2+4x+4-1=

$$\frac{ { x }^{ 3 } +3 }{ { x }^{ 2 } +4x+4 } -1=$$

Evaluate

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

Short Solution Steps

Factor x^{2}+4x+4.

$$\frac{x^{3}+3}{\left(x+2\right)^{2}}-1$$

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

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

Since \frac{x^{3}+3}{\left(x+2\right)^{2}} and \frac{\left(x+2\right)^{2}}{\left(x+2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{3}+3-\left(x+2\right)^{2}.

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

Combine like terms in x^{3}+3-x^{2}-4x-4.

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

Expand \left(x+2\right)^{2}.

$$\frac{x^{3}-1-x^{2}-4x}{x^{2}+4x+4}$$

Expand

$$\frac{x^{3}-x^{2}-4x-1}{x^{2}+4x+4}$$

Short Solution Steps

Factor x^{2}+4x+4.

$$\frac{x^{3}+3}{\left(x+2\right)^{2}}-1$$

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

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

Since \frac{x^{3}+3}{\left(x+2\right)^{2}} and \frac{\left(x+2\right)^{2}}{\left(x+2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{3}+3-\left(x+2\right)^{2}.

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

Combine like terms in x^{3}+3-x^{2}-4x-4.

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

Expand \left(x+2\right)^{2}.

$$\frac{x^{3}-1-x^{2}-4x}{x^{2}+4x+4}$$