For a relation to be not defined/undefined, the denominator must be equal to 0

x² + 2x + 1 = 0

Express 2x as two numbers when you multiply you will get c (1) and when you add you will get b (2)

1 x 1 = 1 and 1 + 1 = 2 hence the number is 1

x² + x + x + 1 = 0

x(x + 1) + 1(x + 1) = 0

(x + 1)(x + 1) = 0

When x + 1 = 0, x = -1

For any equation to be not defined (undefined), the denominator must be 0.

$\frac{\mathrm{x\; +\; 1}}{3x^2\mathrm{-\; 12}}$

For the equation to be not defined, 3x² - 12 = 0

3x² - 12 = 0

Divide both sides by 3

x² - 4 = 0

x² = 4

Take square root of both sides.

x = $\sqrt{4}$ = ± 2, thus -2 or 2

Note:
1. - x - = +
2. - 2 x -2 = + 4

For the equation to be undefined, the denominator must be 0.

2x² - 13x + 15 = 0

Solve for the value of x

2 x 15 = 30

Two numbers when multiplied the result will be 30 and when added the result will be - 13.

The numbers are -10 and - 3.

Express - 13x as -10x - 3x

2x² - 10x - 3x + 15 = 0

Factorize out

2x(x - 5)-3(x-5) = 0
(x - 5)(2x-3) = 0

(x - 5) = 0 or (2x-3) = 0

x - 5 = 0
x = 0 + 5
x = 5

2x-3 = 0
2x = 3

Divide both sides of the equation by 2

x = $\frac{3}{2}$

A function is undefined when the denominator is 0.

x + 1 = 0

x = 0 - 1

x = -1

An expression is undefined when the denominator equals 0.

6x(x + 1) = 0

x + 1 = 0

x = -1

6x = 0

x = $\frac{0}{6}$ = 0

{0, -1}

A function is undefined when the denominator is 0

p² - p = 0

p(p - 1) = 0

p = 0 or p - 1 = 0, p = 1

g:x → $\frac{\mathrm{2x\; -\; 1}}{\mathrm{3x\; -\; 2}}$

For g not defined, the denominator must be 0

3x - 2 = 0

3x = 2

Divide both sides by 3

x = $\frac{2}{3}$