Solve (9a^2/b^2-1)*(6a/3a-b-2)*b/3a+b

$$( \frac { 9 a ^ { 2 } } { b ^ { 2 } } - 1 ) \cdot ( \frac { 6 a } { 3 a - b } - 2 ) \cdot \frac { b } { 3 a + b }$$

Evaluate

$$2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{b^{2}}{b^{2}}.

$$\left(\frac{9a^{2}}{b^{2}}-\frac{b^{2}}{b^{2}}\right)\left(\frac{6a}{3a-b}-2\right)\times \frac{b}{3a+b}$$

Since \frac{9a^{2}}{b^{2}} and \frac{b^{2}}{b^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9a^{2}-b^{2}}{b^{2}}\left(\frac{6a}{3a-b}-2\right)\times \frac{b}{3a+b}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{3a-b}{3a-b}.

$$\frac{9a^{2}-b^{2}}{b^{2}}\left(\frac{6a}{3a-b}-\frac{2\left(3a-b\right)}{3a-b}\right)\times \frac{b}{3a+b}$$

Since \frac{6a}{3a-b} and \frac{2\left(3a-b\right)}{3a-b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9a^{2}-b^{2}}{b^{2}}\times \frac{6a-2\left(3a-b\right)}{3a-b}\times \frac{b}{3a+b}$$

Do the multiplications in 6a-2\left(3a-b\right).

$$\frac{9a^{2}-b^{2}}{b^{2}}\times \frac{6a-6a+2b}{3a-b}\times \frac{b}{3a+b}$$

Combine like terms in 6a-6a+2b.

$$\frac{9a^{2}-b^{2}}{b^{2}}\times \frac{2b}{3a-b}\times \frac{b}{3a+b}$$

Multiply \frac{9a^{2}-b^{2}}{b^{2}} times \frac{2b}{3a-b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9a^{2}-b^{2}\right)\times 2b}{b^{2}\left(3a-b\right)}\times \frac{b}{3a+b}$$

Cancel out b in both numerator and denominator.

$$\frac{2\left(9a^{2}-b^{2}\right)}{b\left(3a-b\right)}\times \frac{b}{3a+b}$$

Multiply \frac{2\left(9a^{2}-b^{2}\right)}{b\left(3a-b\right)} times \frac{b}{3a+b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(9a^{2}-b^{2}\right)b}{b\left(3a-b\right)\left(3a+b\right)}$$

Cancel out b in both numerator and denominator.

$$\frac{2\left(9a^{2}-b^{2}\right)}{\left(3a+b\right)\left(3a-b\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(3a+b\right)\left(3a-b\right) in both numerator and denominator.

$$2$$

Factor

$$2$$