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

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

Evaluate

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

Solution Steps

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

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

Multiply \frac{1}{2x} times \frac{2x}{x+y} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2x in both numerator and denominator.

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

Expand

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

Solution Steps

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

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

Multiply \frac{1}{2x} times \frac{2x}{x+y} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2x in both numerator and denominator.

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