Find the Excluded Values (8ab^2x)/(4a^2b-8ab^2)

$\frac{8 a b^{2} x}{4 a^{2} b - 8 a b^{2}}$

Set the denominator in $\frac{8 a b^{2} x}{4 a^{2} b - 8 a b^{2}}$ equal to $0$ to find where the expression is undefined.

$4 a^{2} b - 8 a b^{2} = 0$

Solve for $a$ .

Factor $4 a b$ out of $4 a^{2} b - 8 a b^{2}$ .

Factor $4 a b$ out of $4 a^{2} b$ .

$4 a b (a) - 8 a b^{2} = 0$

Factor $4 a b$ out of $- 8 a b^{2}$ .

$4 a b (a) + 4 a b (- 2 b) = 0$

Factor $4 a b$ out of $4 a b (a) + 4 a b (- 2 b)$ .

$4 a b (a - 2 b) = 0$

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

$a = 0$

$a - 2 b = 0$

Set $a$ equal to $0$ .

$a = 0$

Set $a - 2 b$ equal to $0$ and solve for $a$ .

Set $a - 2 b$ equal to $0$ .

$a - 2 b = 0$

Add $2 b$ to both sides of the equation.

$a = 2 b$

The final solution is all the values that make $4 a b (a - 2 b) = 0$ true.

$a = 0$

$a = 2 b$

$a = 0$

$a = 2 b$

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 $0$ .

$2 b \leq a \leq 2 b, a = 0$

$[0, 0] \cup [2 b, 2 b]$

Find the Excluded Values (8ab^2x)/(4a^2b-8ab^2)

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