Solve -1/1+(frac{y{x})^2}*y/x^2

$$- \frac { 1 } { 1 + ( \frac { y } { x } ) ^ { 2 } } \times \frac { y } { x ^ { 2 } }$$

Evaluate

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

Solution Steps

To raise \frac{y}{x} to a power, raise both numerator and denominator to the power and then divide.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

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

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

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

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

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

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

Cancel out x^{2} in both numerator and denominator.

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

Expand

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

Solution Steps

To raise \frac{y}{x} to a power, raise both numerator and denominator to the power and then divide.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

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

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

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

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

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

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

Cancel out x^{2} in both numerator and denominator.

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