Solve 5-2y^2/3+y-3y^2-1/y+3

$$\frac { 5 - 2 y ^ { 2 } } { 3 + y } - \frac { 3 y ^ { 2 } - 1 } { y + 3 }$$

Evaluate

$$\frac{6-5y^{2}}{y+3}$$

Short Solution Steps

Since \frac{5-2y^{2}}{3+y} and \frac{3y^{2}-1}{y+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-2y^{2}-\left(3y^{2}-1\right)}{3+y}$$

Do the multiplications in 5-2y^{2}-\left(3y^{2}-1\right).

$$\frac{5-2y^{2}-3y^{2}+1}{3+y}$$

Combine like terms in 5-2y^{2}-3y^{2}+1.

$$\frac{6-5y^{2}}{3+y}$$

Expand

$$\frac{6-5y^{2}}{y+3}$$

Short Solution Steps

Since \frac{5-2y^{2}}{3+y} and \frac{3y^{2}-1}{y+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-2y^{2}-\left(3y^{2}-1\right)}{3+y}$$

Do the multiplications in 5-2y^{2}-\left(3y^{2}-1\right).

$$\frac{5-2y^{2}-3y^{2}+1}{3+y}$$

Combine like terms in 5-2y^{2}-3y^{2}+1.

$$\frac{6-5y^{2}}{3+y}$$