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

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

Evaluate

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

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

Express \frac{\frac{x^{4}}{x+1}}{x^{3}\left(x-1\right)} as a single fraction.

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

Cancel out x^{3} in both numerator and denominator.

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

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

Expand

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

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

Express \frac{\frac{x^{4}}{x+1}}{x^{3}\left(x-1\right)} as a single fraction.

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

Cancel out x^{3} in both numerator and denominator.

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

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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