Solve 3ab/a+b(a/b-b/a)

$$\frac { 3 a b } { a + b } ( \frac { a } { b } - \frac { b } { a } )$$

Evaluate

$$3\left(a-b\right)$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and a is ab. Multiply \frac{a}{b} times \frac{a}{a}. Multiply \frac{b}{a} times \frac{b}{b}.

$$\frac{3ab}{a+b}\left(\frac{aa}{ab}-\frac{bb}{ab}\right)$$

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

$$\frac{3ab}{a+b}\times \frac{aa-bb}{ab}$$

Do the multiplications in aa-bb.

$$\frac{3ab}{a+b}\times \frac{a^{2}-b^{2}}{ab}$$

Multiply \frac{3ab}{a+b} times \frac{a^{2}-b^{2}}{ab} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3ab\left(a^{2}-b^{2}\right)}{\left(a+b\right)ab}$$

Cancel out ab in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{3\left(a+b\right)\left(a-b\right)}{a+b}$$

Cancel out a+b in both numerator and denominator.

$$3\left(a-b\right)$$

Expand the expression.

$$3a-3b$$

Expand

$$3a-3b$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and a is ab. Multiply \frac{a}{b} times \frac{a}{a}. Multiply \frac{b}{a} times \frac{b}{b}.

$$\frac{3ab}{a+b}\left(\frac{aa}{ab}-\frac{bb}{ab}\right)$$

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

$$\frac{3ab}{a+b}\times \frac{aa-bb}{ab}$$

Do the multiplications in aa-bb.

$$\frac{3ab}{a+b}\times \frac{a^{2}-b^{2}}{ab}$$

Multiply \frac{3ab}{a+b} times \frac{a^{2}-b^{2}}{ab} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3ab\left(a^{2}-b^{2}\right)}{\left(a+b\right)ab}$$

Cancel out ab in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{3\left(a+b\right)\left(a-b\right)}{a+b}$$

Cancel out a+b in both numerator and denominator.

$$3\left(a-b\right)$$

Expand the expression.

$$3a-3b$$