Solve 5/x+1/frac{6{y}+2}

$$\frac { \frac { 5 } { x } + 1 } { \frac { 6 } { y } + 2 }$$

Evaluate

$$\frac{y\left(x+5\right)}{2x\left(y+3\right)}$$

Short Solution Steps

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

$$\frac{\frac{5}{x}+\frac{x}{x}}{\frac{6}{y}+2}$$

Since \frac{5}{x} and \frac{x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+x}{x}}{\frac{6}{y}+2}$$

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

$$\frac{\frac{5+x}{x}}{\frac{6}{y}+\frac{2y}{y}}$$

Since \frac{6}{y} and \frac{2y}{y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+x}{x}}{\frac{6+2y}{y}}$$

Divide \frac{5+x}{x} by \frac{6+2y}{y} by multiplying \frac{5+x}{x} by the reciprocal of \frac{6+2y}{y}.

$$\frac{\left(5+x\right)y}{x\left(6+2y\right)}$$

Use the distributive property to multiply 5+x by y.

$$\frac{5y+xy}{x\left(6+2y\right)}$$

Use the distributive property to multiply x by 6+2y.

$$\frac{5y+xy}{6x+2xy}$$

Expand

$$\frac{xy+5y}{2x\left(y+3\right)}$$

Short Solution Steps

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

$$\frac{\frac{5}{x}+\frac{x}{x}}{\frac{6}{y}+2}$$

Since \frac{5}{x} and \frac{x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+x}{x}}{\frac{6}{y}+2}$$

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

$$\frac{\frac{5+x}{x}}{\frac{6}{y}+\frac{2y}{y}}$$

Since \frac{6}{y} and \frac{2y}{y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+x}{x}}{\frac{6+2y}{y}}$$

Divide \frac{5+x}{x} by \frac{6+2y}{y} by multiplying \frac{5+x}{x} by the reciprocal of \frac{6+2y}{y}.

$$\frac{\left(5+x\right)y}{x\left(6+2y\right)}$$

Use the distributive property to multiply 5+x by y.

$$\frac{5y+xy}{x\left(6+2y\right)}$$

Use the distributive property to multiply x by 6+2y.

$$\frac{5y+xy}{6x+2xy}$$