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

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

Evaluate

$$-\frac{3y^{2}-6y-1}{x^{2}+y^{2}}$$

Short Solution Steps

Combine y and 9y to get 10y.

$$\frac{10y+3}{y^{2}+x^{2}}+\frac{-3y^{2}-4y-2}{y^{2}+x^{2}}$$

Since \frac{10y+3}{y^{2}+x^{2}} and \frac{-3y^{2}-4y-2}{y^{2}+x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{10y+3-3y^{2}-4y-2}{y^{2}+x^{2}}$$

Combine like terms in 10y+3-3y^{2}-4y-2.

$$\frac{6y+1-3y^{2}}{y^{2}+x^{2}}$$

Expand

$$\frac{1+6y-3y^{2}}{x^{2}+y^{2}}$$

Short Solution Steps

Combine y and 9y to get 10y.

$$\frac{10y+3}{y^{2}+x^{2}}+\frac{-3y^{2}-4y-2}{y^{2}+x^{2}}$$

Since \frac{10y+3}{y^{2}+x^{2}} and \frac{-3y^{2}-4y-2}{y^{2}+x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{10y+3-3y^{2}-4y-2}{y^{2}+x^{2}}$$

Combine like terms in 10y+3-3y^{2}-4y-2.

$$\frac{6y+1-3y^{2}}{y^{2}+x^{2}}$$