Question

Please find the domain
$\frac{4}{y+2} -\frac{3}{y-2} +\frac{12}{y^{2}-4 }$

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Answer 1

Answer:

$y\in(-\infty, -2)\cup(-2,2)\cup (2,\infty)$

Step-by-step explanation:

Consider expression:

$\dfrac{4}{y+2}-\dfrac{3}{y-2}+\dfrac{12}{y^2-4}$

This expression consists of three fractions.

1st fraction has $y+2$ in denominator. Denominator cannot be equal to 0, so

$y+2\neq 0\\ \\y\neq -2$

2nd fraction has $y-2$ in denominator. Denominator cannot be equal to 0, so

$y-2\neq 0\\ \\y\neq 2$

3rd fraction has $y^2-4$ in denominator. Denominator cannot be equal to 0, so

$y^2-4\neq 0\\ \\y\neq \pm 2$

Hence, the domain is

$y\in(-\infty, -2)\cup(-2,2)\cup (2,\infty)$