Solve frac{(-8x^{2}-11xy+y^{2})+(5x^{2}-2xy-7y^{2})}{(7a^3+8a^2-2a)-(4a^3-3a^2-9a)}

$$\frac { ( - 8 x ^ { 2 } - 11 x y + y ^ { 2 } ) + ( 5 x ^ { 2 } - 2 x y - 7 y ^ { 2 } ) } { ( 7 a ^ { 3 } + 8 a ^ { 2 } - 2 a ) - ( 4 a ^ { 3 } - 3 a ^ { 2 } - 9 a ) }$$

Evaluate

$$-\frac{3x^{2}+13xy+6y^{2}}{a\left(3a^{2}+11a+7\right)}$$

Short Solution Steps

Combine -8x^{2} and 5x^{2} to get -3x^{2}.

$$\frac{-3x^{2}-11xy+y^{2}-2xy-7y^{2}}{7a^{3}+8a^{2}-2a-\left(4a^{3}-3a^{2}-9a\right)}$$

Combine -11xy and -2xy to get -13xy.

$$\frac{-3x^{2}-13xy+y^{2}-7y^{2}}{7a^{3}+8a^{2}-2a-\left(4a^{3}-3a^{2}-9a\right)}$$

Combine y^{2} and -7y^{2} to get -6y^{2}.

$$\frac{-3x^{2}-13xy-6y^{2}}{7a^{3}+8a^{2}-2a-\left(4a^{3}-3a^{2}-9a\right)}$$

To find the opposite of 4a^{3}-3a^{2}-9a, find the opposite of each term.

$$\frac{-3x^{2}-13xy-6y^{2}}{7a^{3}+8a^{2}-2a-4a^{3}+3a^{2}+9a}$$

Combine 7a^{3} and -4a^{3} to get 3a^{3}.

$$\frac{-3x^{2}-13xy-6y^{2}}{3a^{3}+8a^{2}-2a+3a^{2}+9a}$$

Combine 8a^{2} and 3a^{2} to get 11a^{2}.

$$\frac{-3x^{2}-13xy-6y^{2}}{3a^{3}+11a^{2}-2a+9a}$$

Combine -2a and 9a to get 7a.

$$\frac{-3x^{2}-13xy-6y^{2}}{3a^{3}+11a^{2}+7a}$$

Expand

$$-\frac{3x^{2}+13xy+6y^{2}}{3a^{3}+11a^{2}+7a}$$

Short Solution Steps

Combine -8x^{2} and 5x^{2} to get -3x^{2}.

$$\frac{-3x^{2}-11xy+y^{2}-2xy-7y^{2}}{7a^{3}+8a^{2}-2a-\left(4a^{3}-3a^{2}-9a\right)}$$

Combine -11xy and -2xy to get -13xy.

$$\frac{-3x^{2}-13xy+y^{2}-7y^{2}}{7a^{3}+8a^{2}-2a-\left(4a^{3}-3a^{2}-9a\right)}$$

Combine y^{2} and -7y^{2} to get -6y^{2}.

$$\frac{-3x^{2}-13xy-6y^{2}}{7a^{3}+8a^{2}-2a-\left(4a^{3}-3a^{2}-9a\right)}$$

To find the opposite of 4a^{3}-3a^{2}-9a, find the opposite of each term.

$$\frac{-3x^{2}-13xy-6y^{2}}{7a^{3}+8a^{2}-2a-4a^{3}+3a^{2}+9a}$$

Combine 7a^{3} and -4a^{3} to get 3a^{3}.

$$\frac{-3x^{2}-13xy-6y^{2}}{3a^{3}+8a^{2}-2a+3a^{2}+9a}$$

Combine 8a^{2} and 3a^{2} to get 11a^{2}.

$$\frac{-3x^{2}-13xy-6y^{2}}{3a^{3}+11a^{2}-2a+9a}$$

Combine -2a and 9a to get 7a.

$$\frac{-3x^{2}-13xy-6y^{2}}{3a^{3}+11a^{2}+7a}$$