Find the Excluded Values (2a^2+10a)/(3a^2+15a)

$\frac{2 a^{2} + 10 a}{3 a^{2} + 15 a}$

Set the denominator in $\frac{2 a^{2} + 10 a}{3 a^{2} + 15 a}$ equal to $0$ to find where the expression is undefined.

$3 a^{2} + 15 a = 0$

Solve for $a$ .

Factor $3 a$ out of $3 a^{2} + 15 a$ .

Factor $3 a$ out of $3 a^{2}$ .

$3 a (a) + 15 a = 0$

Factor $3 a$ out of $15 a$ .

$3 a (a) + 3 a (5) = 0$

Factor $3 a$ out of $3 a (a) + 3 a (5)$ .

$3 a (a + 5) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$a = 0$

$a + 5 = 0$

Set $a$ equal to $0$ .

$a = 0$

Set $a + 5$ equal to $0$ and solve for $a$ .

Set $a + 5$ equal to $0$ .

$a + 5 = 0$

Subtract $5$ from both sides of the equation.

$a = - 5$

The final solution is all the values that make $3 a (a + 5) = 0$ true.

$a = 0, - 5$

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$a = - 5, a = 0$

Find the Excluded Values (2a^2+10a)/(3a^2+15a)

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