Solve frac{y^{2}+9y+5}{y^{2}+x^2}+-3y^2-4y-2/y^2+x^2

$$\frac { y ^ { 2 } + 9 y + 5 } { y ^ { 2 } + x ^ { 2 } } + \frac { - 3 y ^ { 2 } - 4 y - 2 } { y ^ { 2 } + x ^ { 2 } }$$

Evaluate

$$-\frac{\left(y-3\right)\left(2y+1\right)}{x^{2}+y^{2}}$$

Short Solution Steps

Since \frac{y^{2}+9y+5}{y^{2}+x^{2}} and \frac{-3y^{2}-4y-2}{y^{2}+x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{y^{2}+9y+5-3y^{2}-4y-2}{y^{2}+x^{2}}$$

Combine like terms in y^{2}+9y+5-3y^{2}-4y-2.

$$\frac{-2y^{2}+5y+3}{y^{2}+x^{2}}$$

Expand

$$\frac{3+5y-2y^{2}}{x^{2}+y^{2}}$$

Short Solution Steps

Since \frac{y^{2}+9y+5}{y^{2}+x^{2}} and \frac{-3y^{2}-4y-2}{y^{2}+x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{y^{2}+9y+5-3y^{2}-4y-2}{y^{2}+x^{2}}$$

Combine like terms in y^{2}+9y+5-3y^{2}-4y-2.

$$\frac{-2y^{2}+5y+3}{y^{2}+x^{2}}$$