Solve (2y^2-10y)-(3y^2-9y)/(y-3)(y-5)(3y+8)

$$\frac { ( 2 y ^ { 2 } - 10 y ) - ( 3 y ^ { 2 } - 9 y ) } { ( y - 3 ) ( y - 5 ) ( 3 y + 8 ) }$$

Evaluate

$$-\frac{y\left(y+1\right)}{\left(y-5\right)\left(y-3\right)\left(3y+8\right)}$$

Short Solution Steps

To find the opposite of 3y^{2}-9y, find the opposite of each term.

$$\frac{2y^{2}-10y-3y^{2}+9y}{\left(y-3\right)\left(y-5\right)\left(3y+8\right)}$$

Combine 2y^{2} and -3y^{2} to get -y^{2}.

$$\frac{-y^{2}-10y+9y}{\left(y-3\right)\left(y-5\right)\left(3y+8\right)}$$

Combine -10y and 9y to get -y.

$$\frac{-y^{2}-y}{\left(y-3\right)\left(y-5\right)\left(3y+8\right)}$$

Use the distributive property to multiply y-3 by y-5 and combine like terms.

$$\frac{-y^{2}-y}{\left(y^{2}-8y+15\right)\left(3y+8\right)}$$

Use the distributive property to multiply y^{2}-8y+15 by 3y+8 and combine like terms.

$$\frac{-y^{2}-y}{3y^{3}-16y^{2}-19y+120}$$

Expand

$$-\frac{y^{2}+y}{\left(y-5\right)\left(y-3\right)\left(3y+8\right)}$$

Short Solution Steps

To find the opposite of 3y^{2}-9y, find the opposite of each term.

$$\frac{2y^{2}-10y-3y^{2}+9y}{\left(y-3\right)\left(y-5\right)\left(3y+8\right)}$$

Combine 2y^{2} and -3y^{2} to get -y^{2}.

$$\frac{-y^{2}-10y+9y}{\left(y-3\right)\left(y-5\right)\left(3y+8\right)}$$

Combine -10y and 9y to get -y.

$$\frac{-y^{2}-y}{\left(y-3\right)\left(y-5\right)\left(3y+8\right)}$$

Use the distributive property to multiply y-3 by y-5 and combine like terms.

$$\frac{-y^{2}-y}{\left(y^{2}-8y+15\right)\left(3y+8\right)}$$

Use the distributive property to multiply y^{2}-8y+15 by 3y+8 and combine like terms.

$$\frac{-y^{2}-y}{3y^{3}-16y^{2}-19y+120}$$