Solve a^3+2x^2+x/x^2+x-x/x+1

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

Evaluate

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

Short Solution Steps

Factor x^{2}+x.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x+1\right) and x+1 is x\left(x+1\right). Multiply \frac{x}{x+1} times \frac{x}{x}.

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

Since \frac{a^{3}+2x^{2}+x}{x\left(x+1\right)} and \frac{xx}{x\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in a^{3}+2x^{2}+x-xx.

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

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

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

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

$$\frac{a^{3}+x^{2}+x}{x^{2}+x}$$

Expand

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

Short Solution Steps

Factor x^{2}+x.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x+1\right) and x+1 is x\left(x+1\right). Multiply \frac{x}{x+1} times \frac{x}{x}.

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

Since \frac{a^{3}+2x^{2}+x}{x\left(x+1\right)} and \frac{xx}{x\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in a^{3}+2x^{2}+x-xx.

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

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

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

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

$$\frac{a^{3}+x^{2}+x}{x^{2}+x}$$