Solve b^2/2a-b+4a^2/b-2a

$$\frac { b ^ { 2 } } { 2 a - b } + \frac { 4 a ^ { 2 } } { b - 2 a }$$

Evaluate

$$-\left(2a+b\right)$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a-b and b-2a is 2a-b. Multiply \frac{4a^{2}}{b-2a} times \frac{-1}{-1}.

$$\frac{b^{2}}{2a-b}+\frac{-4a^{2}}{2a-b}$$

Since \frac{b^{2}}{2a-b} and \frac{-4a^{2}}{2a-b} have the same denominator, add them by adding their numerators.

$$\frac{b^{2}-4a^{2}}{2a-b}$$

Factor the expressions that are not already factored in \frac{b^{2}-4a^{2}}{2a-b}.

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

Extract the negative sign in b-2a.

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

Cancel out 2a-b in both numerator and denominator.

$$-\left(2a+b\right)$$

Expand the expression.

$$-2a-b$$

Differentiate w.r.t. b

$$-1$$