Solve (a-1/a)*a^2/a-2

$$( a - \frac { 1 } { a } ) \times \frac { a ^ { 2 } } { a - 2 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{a}{a}.

$$\left(\frac{aa}{a}-\frac{1}{a}\right)\times \frac{a^{2}}{a-2}$$

Since \frac{aa}{a} and \frac{1}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{aa-1}{a}\times \frac{a^{2}}{a-2}$$

Do the multiplications in aa-1.

$$\frac{a^{2}-1}{a}\times \frac{a^{2}}{a-2}$$

Multiply \frac{a^{2}-1}{a} times \frac{a^{2}}{a-2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a in both numerator and denominator.

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

Use the distributive property to multiply a by a^{2}-1.

$$\frac{a^{3}-a}{a-2}$$

Expand

$$\frac{a^{3}-a}{a-2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{a}{a}.

$$\left(\frac{aa}{a}-\frac{1}{a}\right)\times \frac{a^{2}}{a-2}$$

Since \frac{aa}{a} and \frac{1}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{aa-1}{a}\times \frac{a^{2}}{a-2}$$

Do the multiplications in aa-1.

$$\frac{a^{2}-1}{a}\times \frac{a^{2}}{a-2}$$

Multiply \frac{a^{2}-1}{a} times \frac{a^{2}}{a-2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a in both numerator and denominator.

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

Use the distributive property to multiply a by a^{2}-1.

$$\frac{a^{3}-a}{a-2}$$