Solve x-y/x^2yx+y/3xy^25=

$$\frac { x - y } { x ^ { 2 } y } \frac { x + y } { 3 x y ^ { 2 } } 5 =$$

Evaluate

$$\frac{5\left(x^{2}-y^{2}\right)}{3\left(xy\right)^{3}}$$

Short Solution Steps

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

$$\frac{\left(x-y\right)\left(x+y\right)}{x^{2}y\times 3xy^{2}}\times 5$$

Express \frac{\left(x-y\right)\left(x+y\right)}{x^{2}y\times 3xy^{2}}\times 5 as a single fraction.

$$\frac{\left(x-y\right)\left(x+y\right)\times 5}{x^{2}y\times 3xy^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(x-y\right)\left(x+y\right)\times 5}{x^{3}y\times 3y^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(x-y\right)\left(x+y\right)\times 5}{x^{3}y^{3}\times 3}$$

Use the distributive property to multiply x-y by x+y and combine like terms.

$$\frac{\left(x^{2}-y^{2}\right)\times 5}{x^{3}y^{3}\times 3}$$

Use the distributive property to multiply x^{2}-y^{2} by 5.

$$\frac{5x^{2}-5y^{2}}{x^{3}y^{3}\times 3}$$

Expand

$$-\frac{5\left(y^{2}-x^{2}\right)}{3\left(xy\right)^{3}}$$

Short Solution Steps

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

$$\frac{\left(x-y\right)\left(x+y\right)}{x^{2}y\times 3xy^{2}}\times 5$$

Express \frac{\left(x-y\right)\left(x+y\right)}{x^{2}y\times 3xy^{2}}\times 5 as a single fraction.

$$\frac{\left(x-y\right)\left(x+y\right)\times 5}{x^{2}y\times 3xy^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(x-y\right)\left(x+y\right)\times 5}{x^{3}y\times 3y^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(x-y\right)\left(x+y\right)\times 5}{x^{3}y^{3}\times 3}$$

Use the distributive property to multiply x-y by x+y and combine like terms.

$$\frac{\left(x^{2}-y^{2}\right)\times 5}{x^{3}y^{3}\times 3}$$

Use the distributive property to multiply x^{2}-y^{2} by 5.

$$\frac{5x^{2}-5y^{2}}{x^{3}y^{3}\times 3}$$