Solve (frac{x^{2}-y^{2}}{x^{2}+y^{2}}divx^2-y^2/6x)*x^2+y^2/18

$$( \frac { x ^ { 2 } - y ^ { 2 } } { x ^ { 2 } + y ^ { 2 } } \div \frac { x ^ { 2 } - y ^ { 2 } } { 6 x } ) \cdot \frac { x ^ { 2 } + y ^ { 2 } } { 18 }$$

Evaluate

$$\frac{x}{3}$$

Solution Steps

Divide \frac{x^{2}-y^{2}}{x^{2}+y^{2}} by \frac{x^{2}-y^{2}}{6x} by multiplying \frac{x^{2}-y^{2}}{x^{2}+y^{2}} by the reciprocal of \frac{x^{2}-y^{2}}{6x}.

$$\frac{\left(x^{2}-y^{2}\right)\times 6x}{\left(x^{2}+y^{2}\right)\left(x^{2}-y^{2}\right)}\times \frac{x^{2}+y^{2}}{18}$$

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

$$\frac{6x}{x^{2}+y^{2}}\times \frac{x^{2}+y^{2}}{18}$$

Multiply \frac{6x}{x^{2}+y^{2}} times \frac{x^{2}+y^{2}}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6x\left(x^{2}+y^{2}\right)}{\left(x^{2}+y^{2}\right)\times 18}$$

Cancel out 6\left(x^{2}+y^{2}\right) in both numerator and denominator.

$$\frac{x}{3}$$

Expand

$$\frac{x}{3}$$

Solution Steps

Divide \frac{x^{2}-y^{2}}{x^{2}+y^{2}} by \frac{x^{2}-y^{2}}{6x} by multiplying \frac{x^{2}-y^{2}}{x^{2}+y^{2}} by the reciprocal of \frac{x^{2}-y^{2}}{6x}.

$$\frac{\left(x^{2}-y^{2}\right)\times 6x}{\left(x^{2}+y^{2}\right)\left(x^{2}-y^{2}\right)}\times \frac{x^{2}+y^{2}}{18}$$

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

$$\frac{6x}{x^{2}+y^{2}}\times \frac{x^{2}+y^{2}}{18}$$

Multiply \frac{6x}{x^{2}+y^{2}} times \frac{x^{2}+y^{2}}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6x\left(x^{2}+y^{2}\right)}{\left(x^{2}+y^{2}\right)\times 18}$$

Cancel out 6\left(x^{2}+y^{2}\right) in both numerator and denominator.

$$\frac{x}{3}$$