Simplify (p^2-9p)/(p^2-4p-45)-2/(p+5)

$\frac{p^{2} - 9 p}{p^{2} - 4 p - 45} - \frac{2}{p + 5}$

Step 1

Simplify each term.

Factor $p$ out of $p^{2} - 9 p$ .

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

$\frac{p \cdot p - 9 p}{p^{2} - 4 p - 45} - \frac{2}{p + 5}$

Factor $p$ out of $- 9 p$ .

$\frac{p \cdot p + p \cdot - 9}{p^{2} - 4 p - 45} - \frac{2}{p + 5}$

Factor $p$ out of $p \cdot p + p \cdot - 9$ .

$\frac{p (p - 9)}{p^{2} - 4 p - 45} - \frac{2}{p + 5}$

Factor $p^{2} - 4 p - 45$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 45$ and whose sum is $- 4$ .

$- 9, 5$

Write the factored form using these integers.

$\frac{p (p - 9)}{(p - 9) (p + 5)} - \frac{2}{p + 5}$

Cancel the common factor of $p - 9$ .

Cancel the common factor.

$\frac{p (p - 9)}{(p - 9) (p + 5)} - \frac{2}{p + 5}$

Rewrite the expression.

$\frac{p}{p + 5} - \frac{2}{p + 5}$

Step 2

Combine the numerators over the common denominator.

$\frac{p - 2}{p + 5}$

Simplify (p^2-9p)/(p^2-4p-45)-2/(p+5)

Related Questions

Support LCMGCF.com by disabling your adblocker.