Solve (a-4/a)*a^2/a-2

$$( a - \frac { 4 } { a } ) \times \frac { a ^ { 2 } } { a - 2 }$$

Evaluate

$$a\left(a+2\right)$$

Short Solution Steps

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

$$\left(\frac{aa}{a}-\frac{4}{a}\right)\times \frac{a^{2}}{a-2}$$

Since \frac{aa}{a} and \frac{4}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{aa-4}{a}\times \frac{a^{2}}{a-2}$$

Do the multiplications in aa-4.

$$\frac{a^{2}-4}{a}\times \frac{a^{2}}{a-2}$$

Multiply \frac{a^{2}-4}{a} times \frac{a^{2}}{a-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}-4\right)a^{2}}{a\left(a-2\right)}$$

Cancel out a in both numerator and denominator.

$$\frac{a\left(a^{2}-4\right)}{a-2}$$

Factor the expressions that are not already factored.

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

Cancel out a-2 in both numerator and denominator.

$$a\left(a+2\right)$$

Expand the expression.

$$a^{2}+2a$$

Expand

$$a^{2}+2a$$

Short Solution Steps

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

$$\left(\frac{aa}{a}-\frac{4}{a}\right)\times \frac{a^{2}}{a-2}$$

Since \frac{aa}{a} and \frac{4}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{aa-4}{a}\times \frac{a^{2}}{a-2}$$

Do the multiplications in aa-4.

$$\frac{a^{2}-4}{a}\times \frac{a^{2}}{a-2}$$

Multiply \frac{a^{2}-4}{a} times \frac{a^{2}}{a-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}-4\right)a^{2}}{a\left(a-2\right)}$$

Cancel out a in both numerator and denominator.

$$\frac{a\left(a^{2}-4\right)}{a-2}$$

Factor the expressions that are not already factored.

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

Cancel out a-2 in both numerator and denominator.

$$a\left(a+2\right)$$

Expand the expression.

$$a^{2}+2a$$