Solve 2/x^3y+5/xy^4/frac{5{5}-3/2}

$$\frac { \frac { 2 } { x ^ { 3 } y } + \frac { 5 } { x y ^ { 4 } } } { \frac { 5 } { 5 } - \frac { 3 } { 2 } }$$

Evaluate

$$-\frac{4}{yx^{3}}-\frac{10}{xy^{4}}$$

Short Solution Steps

Divide 5 by 5 to get 1.

$$\frac{\frac{2}{x^{3}y}+\frac{5}{xy^{4}}}{1-\frac{3}{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{3}y and xy^{4} is x^{3}y^{4}. Multiply \frac{2}{x^{3}y} times \frac{y^{3}}{y^{3}}. Multiply \frac{5}{xy^{4}} times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{2y^{3}}{x^{3}y^{4}}+\frac{5x^{2}}{x^{3}y^{4}}}{1-\frac{3}{2}}$$

Since \frac{2y^{3}}{x^{3}y^{4}} and \frac{5x^{2}}{x^{3}y^{4}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2y^{3}+5x^{2}}{x^{3}y^{4}}}{1-\frac{3}{2}}$$

Subtract \frac{3}{2} from 1 to get -\frac{1}{2}.

$$\frac{\frac{2y^{3}+5x^{2}}{x^{3}y^{4}}}{-\frac{1}{2}}$$

Divide \frac{2y^{3}+5x^{2}}{x^{3}y^{4}} by -\frac{1}{2} by multiplying \frac{2y^{3}+5x^{2}}{x^{3}y^{4}} by the reciprocal of -\frac{1}{2}.

$$\frac{\left(2y^{3}+5x^{2}\right)\times 2}{x^{3}y^{4}\left(-1\right)}$$

Cancel out -1 in both numerator and denominator.

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

Use the distributive property to multiply 2y^{3}+5x^{2} by -2.

$$\frac{-4y^{3}-10x^{2}}{x^{3}y^{4}}$$

Expand

$$-\frac{4}{yx^{3}}-\frac{10}{xy^{4}}$$

Short Solution Steps

Divide 5 by 5 to get 1.

$$\frac{\frac{2}{x^{3}y}+\frac{5}{xy^{4}}}{1-\frac{3}{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{3}y and xy^{4} is x^{3}y^{4}. Multiply \frac{2}{x^{3}y} times \frac{y^{3}}{y^{3}}. Multiply \frac{5}{xy^{4}} times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{2y^{3}}{x^{3}y^{4}}+\frac{5x^{2}}{x^{3}y^{4}}}{1-\frac{3}{2}}$$

Since \frac{2y^{3}}{x^{3}y^{4}} and \frac{5x^{2}}{x^{3}y^{4}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2y^{3}+5x^{2}}{x^{3}y^{4}}}{1-\frac{3}{2}}$$

Subtract \frac{3}{2} from 1 to get -\frac{1}{2}.

$$\frac{\frac{2y^{3}+5x^{2}}{x^{3}y^{4}}}{-\frac{1}{2}}$$

Divide \frac{2y^{3}+5x^{2}}{x^{3}y^{4}} by -\frac{1}{2} by multiplying \frac{2y^{3}+5x^{2}}{x^{3}y^{4}} by the reciprocal of -\frac{1}{2}.

$$\frac{\left(2y^{3}+5x^{2}\right)\times 2}{x^{3}y^{4}\left(-1\right)}$$

Cancel out -1 in both numerator and denominator.

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

Use the distributive property to multiply 2y^{3}+5x^{2} by -2.

$$\frac{-4y^{3}-10x^{2}}{x^{3}y^{4}}$$