Solve 16/2u^{4-2v^{4}}*u^8-v^8/14u^4+14v^4=?

$$\frac { 16 } { 2 u ^ { 4 } - 2 v ^ { 4 } } \times \frac { u ^ { 8 } - v ^ { 8 } } { 14 u ^ { 4 } + 14 v ^ { 4 } } = ?$$

Evaluate

$$\frac{4}{7}\approx 0.571428571$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{u^{8}-v^{8}}{14u^{4}+14v^{4}}.

$$\frac{16}{2u^{4}-2v^{4}}\times \frac{\left(u+v\right)\left(u-v\right)\left(u^{2}+v^{2}\right)\left(u^{4}+v^{4}\right)}{14\left(u^{4}+v^{4}\right)}$$

Cancel out u^{4}+v^{4} in both numerator and denominator.

$$\frac{16}{2u^{4}-2v^{4}}\times \frac{\left(u+v\right)\left(u-v\right)\left(u^{2}+v^{2}\right)}{14}$$

Multiply \frac{16}{2u^{4}-2v^{4}} times \frac{\left(u+v\right)\left(u-v\right)\left(u^{2}+v^{2}\right)}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\left(u+v\right)\left(u-v\right)\left(u^{2}+v^{2}\right)}{\left(2u^{4}-2v^{4}\right)\times 14}$$

Cancel out 2 in both numerator and denominator.

$$\frac{8\left(u+v\right)\left(u-v\right)\left(u^{2}+v^{2}\right)}{7\left(2u^{4}-2v^{4}\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(u+v\right)\left(u-v\right)\left(u^{2}+v^{2}\right)}{2\times 7\left(u+v\right)\left(u-v\right)\left(u^{2}+v^{2}\right)}$$

Cancel out 2\left(u+v\right)\left(u-v\right)\left(u^{2}+v^{2}\right) in both numerator and denominator.

$$\frac{4}{7}$$

Factor

$$\frac{2 ^ {2}}{7} = 0.5714285714285714$$