How do you simplify and restricted value of $\frac{a^{2} - a - 2}{a^{2} - 13 a + 30}$ $(a^2 - a - 2)/(a^2 - 13a + 30)$ ?

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Answer 1 · 2017-05-19T20:06:43

$\frac{(a + 1) (a - 2)}{(a - 3) (a - 10)}$ $frac((a + 1)(a - 2))((a - 3)(a - 10))$ ; $a \neq 3, 10$ $a ne 3, 10$

We have: $\frac{a^{2} - a - 2}{a^{2} - 13 a + 30}$ $frac(a^(2) - a - 2)(a^(2) - 13 a + 30)$

Let's factorise both the numerator and the denominator using the "middle-term break":

$= \frac{a^{2} + a - 2 a - 2}{a^{2} - 3 a - 10 a + 30}$ $= frac(a^(2) + a - 2 a - 2)(a^(2) - 3 a - 10 a + 30)$

$= \frac{a (a + 1) - 2 (a + 1)}{a (a - 3) - 10 (a - 3)}$ $= frac(a(a + 1) - 2(a + 1))(a(a - 3) - 10(a - 3))$

$= \frac{(a + 1) (a - 2)}{(a - 3) (a - 10)}$ $= frac((a + 1)(a - 2))((a - 3)(a - 10))$

Now let's evaluate the restricted values of $a$ $a$ .

The denominator of the fraction can never be equal to zero:

$\Rightarrow (a - 3) (a - 10) \neq 0$ $Rightarrow (a - 3)(a - 10) ne 0$

Using the null factor law:

$\Rightarrow a - 3 \neq 0, a - 10 \neq 0$ $Rightarrow a - 3 ne 0, a - 10 ne 0$

$\Rightarrow a \neq 3, a \neq 10$ $Rightarrow a ne 3, a ne 10$

$therefore frac(a^(2) - a - 2)(a^(2) - 13 a + 30) = frac((a + 1)(a - 2))((a - 3)(a - 10))$ ; $a ne 3, 10$

How do you simplify and restricted value of (a^2 - a - 2)/(a^2 - 13a + 30)a2−a−2a2−13a+30(a^2 - a - 2)/(a^2 - 13a + 30)?