Solve 1/b-a*-6a+6b-2a^2+2b^2/2

$$\frac { 1 } { b - a } \times \frac { - 6 a + 6 b - 2 a ^ { 2 } + 2 b ^ { 2 } } { 2 }$$

Evaluate

$$a+b+3$$

Short Solution Steps

Divide each term of -6a+6b-2a^{2}+2b^{2} by 2 to get 3b-3a+b^{2}-\left(-a\right)^{2}.

$$\frac{1}{b-a}\left(3b-3a+b^{2}-\left(-a\right)^{2}\right)$$

Express \frac{1}{b-a}\left(3b-3a+b^{2}-\left(-a\right)^{2}\right) as a single fraction.

$$\frac{3b-3a+b^{2}-\left(-a\right)^{2}}{b-a}$$

Expand \left(-a\right)^{2}.

$$\frac{3b-3a+b^{2}-\left(-1\right)^{2}a^{2}}{b-a}$$

Calculate -1 to the power of 2 and get 1.

$$\frac{3b-3a+b^{2}-a^{2}}{b-a}$$

Factor the expressions that are not already factored.

$$\frac{\left(-a+b\right)\left(a+b+3\right)}{-a+b}$$

Cancel out -a+b in both numerator and denominator.

$$a+b+3$$

Expand

$$a+b+3$$

Short Solution Steps

Divide each term of -6a+6b-2a^{2}+2b^{2} by 2 to get 3b-3a+b^{2}-\left(-a\right)^{2}.

$$\frac{1}{b-a}\left(3b-3a+b^{2}-\left(-a\right)^{2}\right)$$

Express \frac{1}{b-a}\left(3b-3a+b^{2}-\left(-a\right)^{2}\right) as a single fraction.

$$\frac{3b-3a+b^{2}-\left(-a\right)^{2}}{b-a}$$

Expand \left(-a\right)^{2}.

$$\frac{3b-3a+b^{2}-\left(-1\right)^{2}a^{2}}{b-a}$$

Calculate -1 to the power of 2 and get 1.

$$\frac{3b-3a+b^{2}-a^{2}}{b-a}$$

Factor the expressions that are not already factored.

$$\frac{\left(-a+b\right)\left(a+b+3\right)}{-a+b}$$

Cancel out -a+b in both numerator and denominator.

$$a+b+3$$