Solve x^2y^2/frac{1{x^3}+1/y^3}

$$\frac { x ^ { 2 } y ^ { 2 } } { \frac { 1 } { x ^ { 3 } } + \frac { 1 } { y ^ { 3 } } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{3} and y^{3} is x^{3}y^{3}. Multiply \frac{1}{x^{3}} times \frac{y^{3}}{y^{3}}. Multiply \frac{1}{y^{3}} times \frac{x^{3}}{x^{3}}.

$$\frac{x^{2}y^{2}}{\frac{y^{3}}{x^{3}y^{3}}+\frac{x^{3}}{x^{3}y^{3}}}$$

Since \frac{y^{3}}{x^{3}y^{3}} and \frac{x^{3}}{x^{3}y^{3}} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}y^{2}}{\frac{y^{3}+x^{3}}{x^{3}y^{3}}}$$

Divide x^{2}y^{2} by \frac{y^{3}+x^{3}}{x^{3}y^{3}} by multiplying x^{2}y^{2} by the reciprocal of \frac{y^{3}+x^{3}}{x^{3}y^{3}}.

$$\frac{x^{2}y^{2}x^{3}y^{3}}{y^{3}+x^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{x^{5}y^{5}}{y^{3}+x^{3}}$$

Differentiate w.r.t. x

$$\frac{\left(2x^{3}+5y^{3}\right)x^{4}y^{5}}{\left(x^{3}+y^{3}\right)^{2}}$$