Solve lambda^2-5kappalambda+4kappa^2/2kappa^2-kappalambda-lambda^2

$$\frac { \lambda ^ { 2 } - 5 \kappa \lambda + 4 \kappa ^ { 2 } } { 2 \kappa ^ { 2 } - \kappa \lambda - \lambda ^ { 2 } }$$

Evaluate

$$-\frac{\lambda -4\kappa }{2\kappa +\lambda }$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(-4\kappa +\lambda \right)\left(-\kappa +\lambda \right)}{\left(\kappa -\lambda \right)\left(2\kappa +\lambda \right)}$$

Extract the negative sign in \lambda -\kappa .

$$\frac{-\left(\kappa -\lambda \right)\left(-4\kappa +\lambda \right)}{\left(\kappa -\lambda \right)\left(2\kappa +\lambda \right)}$$

Cancel out \kappa -\lambda in both numerator and denominator.

$$\frac{-\left(-4\kappa +\lambda \right)}{2\kappa +\lambda }$$

Expand the expression.

$$\frac{4\kappa -\lambda }{2\kappa +\lambda }$$

Expand

$$\frac{4\kappa -\lambda }{2\kappa +\lambda }$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(-4\kappa +\lambda \right)\left(-\kappa +\lambda \right)}{\left(\kappa -\lambda \right)\left(2\kappa +\lambda \right)}$$

Extract the negative sign in \lambda -\kappa .

$$\frac{-\left(\kappa -\lambda \right)\left(-4\kappa +\lambda \right)}{\left(\kappa -\lambda \right)\left(2\kappa +\lambda \right)}$$

Cancel out \kappa -\lambda in both numerator and denominator.

$$\frac{-\left(-4\kappa +\lambda \right)}{2\kappa +\lambda }$$

Expand the expression.

$$\frac{4\kappa -\lambda }{2\kappa +\lambda }$$