# How do you simplify and find the excluded values of (x^2+5x+4)/(x^2-x-72)?

Jun 20, 2016

the exclude values are $x = 9 \mathmr{and} x = - 8$

#### Explanation:

Try the factoring of both trynomials by using the following rule:

in a trynomial ${x}^{2} + s x + p$ find two numbers a and b of which s is the sum and p the product, then factor in this way:

$\left(x + a\right) \left(x + b\right)$

so

${x}^{2} + 5 x + 4 = \left(x + 1\right) \left(x + 4\right)$
and
${x}^{2} - x - 72 = \left(x - 9\right) \left(x + 8\right)$

The fraction is equivalent to the following one:

$\frac{\left(x + 1\right) \left(x + 4\right)}{\left(x - 9\right) \left(x + 8\right)}$

but you cannot symplify the expression!

The excluded values are those ones that make null the denominator:

$\left(x - 9\right) \left(x + 8\right)$

that are $x = 9 \mathmr{and} x = - 8$