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43. What is the value of [tex]$z$[/tex] such that [tex]$\frac{2}{z-3}$[/tex] is undefined?

Sagot :

To determine the value of [tex]\( z \)[/tex] that makes the expression [tex]\( \frac{2}{z-3} \)[/tex] undefined, we need to focus on the denominator of the fraction.

In mathematics, a fraction is undefined when its denominator is equal to zero, as division by zero is not allowed.

Given the expression [tex]\( \frac{2}{z-3} \)[/tex], the denominator is [tex]\( z-3 \)[/tex].

To find the value of [tex]\( z \)[/tex] that makes the denominator zero, we set the denominator equal to zero and solve for [tex]\( z \)[/tex]:

[tex]\[ z - 3 = 0 \][/tex]

Adding 3 to both sides of the equation gives:

[tex]\[ z = 3 \][/tex]

Thus, the value of [tex]\( z \)[/tex] that makes the expression [tex]\( \frac{2}{z-3} \)[/tex] undefined is [tex]\( z = 3 \)[/tex].