Solve y^2-4/x+1:y+2/1-y^2

$$\frac { y ^ { 2 } - 4 } { x + 1 } : \frac { y + 2 } { 1 - y ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Divide \frac{y^{2}-4}{x+1} by \frac{y+2}{1-y^{2}} by multiplying \frac{y^{2}-4}{x+1} by the reciprocal of \frac{y+2}{1-y^{2}}.

$$\frac{\left(y^{2}-4\right)\left(1-y^{2}\right)}{\left(x+1\right)\left(y+2\right)}$$

Factor the expressions that are not already factored.

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

Cancel out y+2 in both numerator and denominator.

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

Expand the expression.

$$\frac{-y^{3}+2y^{2}+y-2}{x+1}$$

Expand

$$\frac{-y^{3}+2y^{2}+y-2}{x+1}$$

Short Solution Steps

Divide \frac{y^{2}-4}{x+1} by \frac{y+2}{1-y^{2}} by multiplying \frac{y^{2}-4}{x+1} by the reciprocal of \frac{y+2}{1-y^{2}}.

$$\frac{\left(y^{2}-4\right)\left(1-y^{2}\right)}{\left(x+1\right)\left(y+2\right)}$$

Factor the expressions that are not already factored.

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

Cancel out y+2 in both numerator and denominator.

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

Expand the expression.

$$\frac{-y^{3}+2y^{2}+y-2}{x+1}$$