Solve (y/9+x)(5-x/y)+(y-x/9+x)

$$( \frac { y } { 9 + x } ) ( 5 - \frac { x } { y } ) + ( \frac { y - x } { 9 + x } )$$

Evaluate

$$\frac{2\left(3y-x\right)}{x+9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{y}{y}.

$$\frac{y}{9+x}\left(\frac{5y}{y}-\frac{x}{y}\right)+\frac{y-x}{9+x}$$

Since \frac{5y}{y} and \frac{x}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y}{9+x}\times \frac{5y-x}{y}+\frac{y-x}{9+x}$$

Multiply \frac{y}{9+x} times \frac{5y-x}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{y\left(5y-x\right)}{\left(9+x\right)y}+\frac{y-x}{9+x}$$

Cancel out y in both numerator and denominator.

$$\frac{-x+5y}{x+9}+\frac{y-x}{9+x}$$

Since \frac{-x+5y}{x+9} and \frac{y-x}{9+x} have the same denominator, add them by adding their numerators.

$$\frac{-x+5y+y-x}{x+9}$$

Combine like terms in -x+5y+y-x.

$$\frac{-2x+6y}{x+9}$$

Expand

$$-\frac{2\left(x-3y\right)}{x+9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{y}{y}.

$$\frac{y}{9+x}\left(\frac{5y}{y}-\frac{x}{y}\right)+\frac{y-x}{9+x}$$

Since \frac{5y}{y} and \frac{x}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y}{9+x}\times \frac{5y-x}{y}+\frac{y-x}{9+x}$$

Multiply \frac{y}{9+x} times \frac{5y-x}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{y\left(5y-x\right)}{\left(9+x\right)y}+\frac{y-x}{9+x}$$

Cancel out y in both numerator and denominator.

$$\frac{-x+5y}{x+9}+\frac{y-x}{9+x}$$

Since \frac{-x+5y}{x+9} and \frac{y-x}{9+x} have the same denominator, add them by adding their numerators.

$$\frac{-x+5y+y-x}{x+9}$$

Combine like terms in -x+5y+y-x.

$$\frac{-2x+6y}{x+9}$$