Basic Math Examples

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

Step 1

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{6}{p^{2} - 6} + \frac{p^{2}}{- 1 (- 6) - p^{2}}$

Step 2

Factor $- 1$ out of $- p^{2}$ .

$\frac{6}{p^{2} - 6} + \frac{p^{2}}{- 1 (- 6) - (p^{2})}$

Step 3

Factor $- 1$ out of $- 1 (- 6) - (p^{2})$ .

$\frac{6}{p^{2} - 6} + \frac{p^{2}}{- 1 (- 6 + p^{2})}$

Step 4

Simplify the expression.

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Step 4.1

Move a negative from the denominator of $\frac{p^{2}}{- 1 (- 6 + p^{2})}$ to the numerator.

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

Step 4.2

Reorder terms.

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

Step 5

Combine the numerators over the common denominator.

$\frac{6 - p^{2}}{p^{2} - 6}$

Step 6

Cancel the common factor of $6 - p^{2}$ and $p^{2} - 6$ .

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Step 6.1

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{- 1 (- 6) - p^{2}}{p^{2} - 6}$

Step 6.2

Factor $- 1$ out of $- p^{2}$ .

$\frac{- 1 (- 6) - (p^{2})}{p^{2} - 6}$

Step 6.3

Factor $- 1$ out of $- 1 (- 6) - (p^{2})$ .

$\frac{- 1 (- 6 + p^{2})}{p^{2} - 6}$

Step 6.4

Reorder terms.

$\frac{- 1 (p^{2} - 6)}{p^{2} - 6}$

Step 6.5

Cancel the common factor.

$\frac{- 1 (p^{2} - 6)}{p^{2} - 6}$

Step 6.6

Divide $- 1$ by $1$ .

$- 1$