Solve (x^2-x-3)/x^2+1*x^2+x+1

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

Evaluate

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

Short Solution Steps

Express \frac{x^{2}-x-3}{x^{2}+1}x^{2} as a single fraction.

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

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

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

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

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

Do the multiplications in \left(x^{2}-x-3\right)x^{2}+\left(x+1\right)\left(x^{2}+1\right).

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

Combine like terms in x^{4}-x^{3}-3x^{2}+x^{3}+x+x^{2}+1.

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

Expand

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

Short Solution Steps

Express \frac{x^{2}-x-3}{x^{2}+1}x^{2} as a single fraction.

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

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

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

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

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

Do the multiplications in \left(x^{2}-x-3\right)x^{2}+\left(x+1\right)\left(x^{2}+1\right).

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

Combine like terms in x^{4}-x^{3}-3x^{2}+x^{3}+x+x^{2}+1.

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