Solve 5y/4x+2x/3y-y^2/12xy

$$\frac { 5 y } { 4 x } + \frac { 2 x } { 3 y } - \frac { y ^ { 2 } } { 12 x y }$$

Evaluate

$$\frac{4x^{2}+7y^{2}}{6xy}$$

Short Solution Steps

Cancel out y in both numerator and denominator.

$$\frac{5y}{4x}+\frac{2x}{3y}-\frac{y}{12x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4x and 3y is 12xy. Multiply \frac{5y}{4x} times \frac{3y}{3y}. Multiply \frac{2x}{3y} times \frac{4x}{4x}.

$$\frac{5y\times 3y}{12xy}+\frac{2x\times 4x}{12xy}-\frac{y}{12x}$$

Since \frac{5y\times 3y}{12xy} and \frac{2x\times 4x}{12xy} have the same denominator, add them by adding their numerators.

$$\frac{5y\times 3y+2x\times 4x}{12xy}-\frac{y}{12x}$$

Do the multiplications in 5y\times 3y+2x\times 4x.

$$\frac{15y^{2}+8x^{2}}{12xy}-\frac{y}{12x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12xy and 12x is 12xy. Multiply \frac{y}{12x} times \frac{y}{y}.

$$\frac{15y^{2}+8x^{2}}{12xy}-\frac{yy}{12xy}$$

Since \frac{15y^{2}+8x^{2}}{12xy} and \frac{yy}{12xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15y^{2}+8x^{2}-yy}{12xy}$$

Do the multiplications in 15y^{2}+8x^{2}-yy.

$$\frac{15y^{2}+8x^{2}-y^{2}}{12xy}$$

Combine like terms in 15y^{2}+8x^{2}-y^{2}.

$$\frac{14y^{2}+8x^{2}}{12xy}$$

Factor the expressions that are not already factored in \frac{14y^{2}+8x^{2}}{12xy}.

$$\frac{2\left(4x^{2}+7y^{2}\right)}{12xy}$$

Cancel out 2 in both numerator and denominator.

$$\frac{4x^{2}+7y^{2}}{6xy}$$

Factor

$$\frac{4x^{2}+7y^{2}}{6xy}$$