Solve 4/p-p^2-49/2p^4:p+7/p^3

$$\frac { 4 } { p } - \frac { p ^ { 2 } - 49 } { 2 p ^ { 4 } } : \frac { p + 7 } { p ^ { 3 } }$$

Evaluate

$$-\frac{1}{2}+\frac{15}{2p}$$

Short Solution Steps

Divide \frac{p^{2}-49}{2p^{4}} by \frac{p+7}{p^{3}} by multiplying \frac{p^{2}-49}{2p^{4}} by the reciprocal of \frac{p+7}{p^{3}}.

$$\frac{4}{p}-\frac{\left(p^{2}-49\right)p^{3}}{2p^{4}\left(p+7\right)}$$

Cancel out p^{3} in both numerator and denominator.

$$\frac{4}{p}-\frac{p^{2}-49}{2p\left(p+7\right)}$$

Factor the expressions that are not already factored in \frac{p^{2}-49}{2p\left(p+7\right)}.

$$\frac{4}{p}-\frac{\left(p-7\right)\left(p+7\right)}{2p\left(p+7\right)}$$

Cancel out p+7 in both numerator and denominator.

$$\frac{4}{p}-\frac{p-7}{2p}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p and 2p is 2p. Multiply \frac{4}{p} times \frac{2}{2}.

$$\frac{4\times 2}{2p}-\frac{p-7}{2p}$$

Since \frac{4\times 2}{2p} and \frac{p-7}{2p} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\times 2-\left(p-7\right)}{2p}$$

Do the multiplications in 4\times 2-\left(p-7\right).

$$\frac{8-p+7}{2p}$$

Combine like terms in 8-p+7.

$$\frac{15-p}{2p}$$

Expand

$$-\frac{1}{2}+\frac{15}{2p}$$

Short Solution Steps

Divide \frac{p^{2}-49}{2p^{4}} by \frac{p+7}{p^{3}} by multiplying \frac{p^{2}-49}{2p^{4}} by the reciprocal of \frac{p+7}{p^{3}}.

$$\frac{4}{p}-\frac{\left(p^{2}-49\right)p^{3}}{2p^{4}\left(p+7\right)}$$

Cancel out p^{3} in both numerator and denominator.

$$\frac{4}{p}-\frac{p^{2}-49}{2p\left(p+7\right)}$$

Factor the expressions that are not already factored in \frac{p^{2}-49}{2p\left(p+7\right)}.

$$\frac{4}{p}-\frac{\left(p-7\right)\left(p+7\right)}{2p\left(p+7\right)}$$

Cancel out p+7 in both numerator and denominator.

$$\frac{4}{p}-\frac{p-7}{2p}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p and 2p is 2p. Multiply \frac{4}{p} times \frac{2}{2}.

$$\frac{4\times 2}{2p}-\frac{p-7}{2p}$$

Since \frac{4\times 2}{2p} and \frac{p-7}{2p} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\times 2-\left(p-7\right)}{2p}$$

Do the multiplications in 4\times 2-\left(p-7\right).

$$\frac{8-p+7}{2p}$$

Combine like terms in 8-p+7.

$$\frac{15-p}{2p}$$