Solve y/x+y-2y^2/x+y+5y^2-8y/x+y

$$\frac { y } { x + y } - \frac { 2 y ^ { 2 } } { x + y } + \frac { 5 y ^ { 2 } - 8 y } { x + y }$$

Evaluate

$$\frac{y\left(3y-7\right)}{x+y}$$

Short Solution Steps

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

$$\frac{y-2y^{2}}{x+y}+\frac{5y^{2}-8y}{x+y}$$

Since \frac{y-2y^{2}}{x+y} and \frac{5y^{2}-8y}{x+y} have the same denominator, add them by adding their numerators.

$$\frac{y-2y^{2}+5y^{2}-8y}{x+y}$$

Combine like terms in y-2y^{2}+5y^{2}-8y.

$$\frac{-7y+3y^{2}}{x+y}$$

Expand

$$\frac{3y^{2}-7y}{x+y}$$

Short Solution Steps

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

$$\frac{y-2y^{2}}{x+y}+\frac{5y^{2}-8y}{x+y}$$

Since \frac{y-2y^{2}}{x+y} and \frac{5y^{2}-8y}{x+y} have the same denominator, add them by adding their numerators.

$$\frac{y-2y^{2}+5y^{2}-8y}{x+y}$$

Combine like terms in y-2y^{2}+5y^{2}-8y.

$$\frac{-7y+3y^{2}}{x+y}$$