Solve frac{p^{3}+r^{3}-q^3+3pqr}{p^2+q^2+r^2+pq+qr-rp}=

$$\frac { p ^ { 3 } + r ^ { 3 } - q ^ { 3 } + 3 p q r } { p ^ { 2 } + q ^ { 2 } + r ^ { 2 } + p q + q r - r p } =$$

Evaluate

$$p-q+r$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(p-q+r\right)\left(p^{2}+pq-pr+q^{2}+qr+r^{2}\right)}{p^{2}+pq-pr+q^{2}+qr+r^{2}}$$

Cancel out p^{2}+pq-pr+q^{2}+qr+r^{2} in both numerator and denominator.

$$p-q+r$$

Expand

$$p-q+r$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(p-q+r\right)\left(p^{2}+pq-pr+q^{2}+qr+r^{2}\right)}{p^{2}+pq-pr+q^{2}+qr+r^{2}}$$

Cancel out p^{2}+pq-pr+q^{2}+qr+r^{2} in both numerator and denominator.

$$p-q+r$$