Solve 1-1-2y^2/1-y+y

$$1 - \frac { 1 - 2 y ^ { 2 } } { 1 - y } + y$$

Evaluate

$$\frac{y^{2}}{1-y}$$

Short Solution Steps

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

$$\frac{\left(1+y\right)\left(1-y\right)}{1-y}-\frac{1-2y^{2}}{1-y}$$

Since \frac{\left(1+y\right)\left(1-y\right)}{1-y} and \frac{1-2y^{2}}{1-y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(1+y\right)\left(1-y\right)-\left(1-2y^{2}\right)}{1-y}$$

Do the multiplications in \left(1+y\right)\left(1-y\right)-\left(1-2y^{2}\right).

$$\frac{1-y+y-y^{2}-1+2y^{2}}{1-y}$$

Combine like terms in 1-y+y-y^{2}-1+2y^{2}.

$$\frac{y^{2}}{1-y}$$

Expand

$$\frac{y^{2}}{1-y}$$

Short Solution Steps

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

$$\frac{\left(1+y\right)\left(1-y\right)}{1-y}-\frac{1-2y^{2}}{1-y}$$

Since \frac{\left(1+y\right)\left(1-y\right)}{1-y} and \frac{1-2y^{2}}{1-y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(1+y\right)\left(1-y\right)-\left(1-2y^{2}\right)}{1-y}$$

Do the multiplications in \left(1+y\right)\left(1-y\right)-\left(1-2y^{2}\right).

$$\frac{1-y+y-y^{2}-1+2y^{2}}{1-y}$$

Combine like terms in 1-y+y-y^{2}-1+2y^{2}.

$$\frac{y^{2}}{1-y}$$