Solve 6ab/a+6b*(a/6b-6b/a)

$$\frac { 6 a b } { a + 6 b } \cdot ( \frac { a } { 6 b } - \frac { 6 b } { a } )$$

Evaluate

$$a-6b$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6b and a is 6ab. Multiply \frac{a}{6b} times \frac{a}{a}. Multiply \frac{6b}{a} times \frac{6b}{6b}.

$$\frac{6ab}{a+6b}\left(\frac{aa}{6ab}-\frac{6b\times 6b}{6ab}\right)$$

Since \frac{aa}{6ab} and \frac{6b\times 6b}{6ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6ab}{a+6b}\times \frac{aa-6b\times 6b}{6ab}$$

Do the multiplications in aa-6b\times 6b.

$$\frac{6ab}{a+6b}\times \frac{a^{2}-36b^{2}}{6ab}$$

Multiply \frac{6ab}{a+6b} times \frac{a^{2}-36b^{2}}{6ab} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6ab\left(a^{2}-36b^{2}\right)}{\left(a+6b\right)\times 6ab}$$

Cancel out 6ab in both numerator and denominator.

$$\frac{a^{2}-36b^{2}}{a+6b}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-6b\right)\left(a+6b\right)}{a+6b}$$

Cancel out a+6b in both numerator and denominator.

$$a-6b$$

Expand

$$a-6b$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6b and a is 6ab. Multiply \frac{a}{6b} times \frac{a}{a}. Multiply \frac{6b}{a} times \frac{6b}{6b}.

$$\frac{6ab}{a+6b}\left(\frac{aa}{6ab}-\frac{6b\times 6b}{6ab}\right)$$

Since \frac{aa}{6ab} and \frac{6b\times 6b}{6ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6ab}{a+6b}\times \frac{aa-6b\times 6b}{6ab}$$

Do the multiplications in aa-6b\times 6b.

$$\frac{6ab}{a+6b}\times \frac{a^{2}-36b^{2}}{6ab}$$

Multiply \frac{6ab}{a+6b} times \frac{a^{2}-36b^{2}}{6ab} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6ab\left(a^{2}-36b^{2}\right)}{\left(a+6b\right)\times 6ab}$$

Cancel out 6ab in both numerator and denominator.

$$\frac{a^{2}-36b^{2}}{a+6b}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-6b\right)\left(a+6b\right)}{a+6b}$$

Cancel out a+6b in both numerator and denominator.

$$a-6b$$