Solve p^2+p^4/p^6+p^0*p/2

$$\frac { p ^ { 2 } + p ^ { 4 } } { p ^ { 6 } + p ^ { 0 } } \cdot \frac { p } { 2 }$$

Evaluate

$$\frac{p^{3}}{2\left(p^{4}-p^{2}+1\right)}$$

Short Solution Steps

Calculate p to the power of 0 and get 1.

$$\frac{p^{2}+p^{4}}{p^{6}+1}\times \frac{p}{2}$$

Factor the expressions that are not already factored in \frac{p^{2}+p^{4}}{p^{6}+1}.

$$\frac{p^{2}\left(p^{2}+1\right)}{\left(p^{2}+1\right)\left(p^{4}-p^{2}+1\right)}\times \frac{p}{2}$$

Cancel out p^{2}+1 in both numerator and denominator.

$$\frac{p^{2}}{p^{4}-p^{2}+1}\times \frac{p}{2}$$

Multiply \frac{p^{2}}{p^{4}-p^{2}+1} times \frac{p}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{p^{2}p}{\left(p^{4}-p^{2}+1\right)\times 2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{p^{3}}{\left(p^{4}-p^{2}+1\right)\times 2}$$

Use the distributive property to multiply p^{4}-p^{2}+1 by 2.

$$\frac{p^{3}}{2p^{4}-2p^{2}+2}$$

Factor

$$\frac{p^{3}}{2\left(p^{4}-p^{2}+1\right)}$$