Solve 5+p^2/p^2-36-p/6+p

$$\frac { 5 + p ^ { 2 } } { p ^ { 2 } - 36 } - \frac { p } { 6 + p }$$

Evaluate

$$\frac{6p+5}{p^{2}-36}$$

Short Solution Steps

Factor p^{2}-36.

$$\frac{5+p^{2}}{\left(p-6\right)\left(p+6\right)}-\frac{p}{6+p}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(p-6\right)\left(p+6\right) and 6+p is \left(p-6\right)\left(p+6\right). Multiply \frac{p}{6+p} times \frac{p-6}{p-6}.

$$\frac{5+p^{2}}{\left(p-6\right)\left(p+6\right)}-\frac{p\left(p-6\right)}{\left(p-6\right)\left(p+6\right)}$$

Since \frac{5+p^{2}}{\left(p-6\right)\left(p+6\right)} and \frac{p\left(p-6\right)}{\left(p-6\right)\left(p+6\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5+p^{2}-p\left(p-6\right)}{\left(p-6\right)\left(p+6\right)}$$

Do the multiplications in 5+p^{2}-p\left(p-6\right).

$$\frac{5+p^{2}-p^{2}+6p}{\left(p-6\right)\left(p+6\right)}$$

Combine like terms in 5+p^{2}-p^{2}+6p.

$$\frac{5+6p}{\left(p-6\right)\left(p+6\right)}$$

Expand \left(p-6\right)\left(p+6\right).

$$\frac{5+6p}{p^{2}-36}$$

Expand

$$\frac{6p+5}{p^{2}-36}$$

Short Solution Steps

Factor p^{2}-36.

$$\frac{5+p^{2}}{\left(p-6\right)\left(p+6\right)}-\frac{p}{6+p}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(p-6\right)\left(p+6\right) and 6+p is \left(p-6\right)\left(p+6\right). Multiply \frac{p}{6+p} times \frac{p-6}{p-6}.

$$\frac{5+p^{2}}{\left(p-6\right)\left(p+6\right)}-\frac{p\left(p-6\right)}{\left(p-6\right)\left(p+6\right)}$$

Since \frac{5+p^{2}}{\left(p-6\right)\left(p+6\right)} and \frac{p\left(p-6\right)}{\left(p-6\right)\left(p+6\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5+p^{2}-p\left(p-6\right)}{\left(p-6\right)\left(p+6\right)}$$

Do the multiplications in 5+p^{2}-p\left(p-6\right).

$$\frac{5+p^{2}-p^{2}+6p}{\left(p-6\right)\left(p+6\right)}$$

Combine like terms in 5+p^{2}-p^{2}+6p.

$$\frac{5+6p}{\left(p-6\right)\left(p+6\right)}$$

Expand \left(p-6\right)\left(p+6\right).

$$\frac{5+6p}{p^{2}-36}$$