Solve 1/+2aquadtext{(6)}x^2-4y^2/3xy^2*xy/x+2y

$$\frac { 1 } { + 2 a } \quad \text { (6) } \frac { x ^ { 2 } - 4 y ^ { 2 } } { 3 x y ^ { 2 } } \cdot \frac { x y } { x + 2 y }$$

Evaluate

$$\frac{x-2y}{ay}$$

Short Solution Steps

Express \frac{1}{2a}\times 6 as a single fraction.

$$\frac{6}{2a}\times \frac{x^{2}-4y^{2}}{3xy^{2}}\times \frac{xy}{x+2y}$$

Multiply \frac{6}{2a} times \frac{x^{2}-4y^{2}}{3xy^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6\left(x^{2}-4y^{2}\right)}{2a\times 3xy^{2}}\times \frac{xy}{x+2y}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{x^{2}-4y^{2}}{axy^{2}}\times \frac{xy}{x+2y}$$

Multiply \frac{x^{2}-4y^{2}}{axy^{2}} times \frac{xy}{x+2y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-4y^{2}\right)xy}{axy^{2}\left(x+2y\right)}$$

Cancel out xy in both numerator and denominator.

$$\frac{x^{2}-4y^{2}}{ay\left(x+2y\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-2y\right)\left(x+2y\right)}{ay\left(x+2y\right)}$$

Cancel out x+2y in both numerator and denominator.

$$\frac{x-2y}{ay}$$

Factor

$$\frac{x-2y}{ay}$$