Solve frac{(b-a)(b+a)c^{2}}{(c^{2}-b^{2})^2-(c^2-a^2)^2}

$$\frac { ( b - a ) ( b + a ) c ^ { 2 } } { ( c ^ { 2 } - b ^ { 2 } ) ^ { 2 } - ( c ^ { 2 } - a ^ { 2 } ) ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Extract the negative sign in b+a.

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

Cancel out \left(-a+b\right)\left(-a-b\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Extract the negative sign in b+a.

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

Cancel out \left(-a+b\right)\left(-a-b\right) in both numerator and denominator.

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