Solve -2/1-aquadx^2-2x+a

$$- \frac { 2 } { 1 - a } \quad x ^ { 2 } - 2 x + a$$

Evaluate

$$\frac{a-a^{2}-2x+2ax-2x^{2}}{1-a}$$

Short Solution Steps

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

$$\frac{-2x^{2}}{1-a}-2x+a$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2x+a times \frac{1-a}{1-a}.

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

Since \frac{-2x^{2}}{1-a} and \frac{\left(-2x+a\right)\left(1-a\right)}{1-a} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -2x^{2}+\left(-2x+a\right)\left(1-a\right).

$$\frac{-2x^{2}-2x+2xa+a-a^{2}}{1-a}$$

Differentiate w.r.t. x

$$\frac{2\left(-2x+a-1\right)}{1-a}$$