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

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

Evaluate

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

Short Solution Steps

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

$$\frac{\frac{xx}{xy}+\frac{y}{xy}}{\frac{3x}{2y}}$$

Since \frac{xx}{xy} and \frac{y}{xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{xx+y}{xy}}{\frac{3x}{2y}}$$

Do the multiplications in xx+y.

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

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

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

Cancel out y in both numerator and denominator.

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

Multiply x and x to get x^{2}.

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

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

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

Expand

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

Short Solution Steps

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

$$\frac{\frac{xx}{xy}+\frac{y}{xy}}{\frac{3x}{2y}}$$

Since \frac{xx}{xy} and \frac{y}{xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{xx+y}{xy}}{\frac{3x}{2y}}$$

Do the multiplications in xx+y.

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

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

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

Cancel out y in both numerator and denominator.

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

Multiply x and x to get x^{2}.

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

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

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