Find the domain of the Equation: (24:3t+4)/(24y+48) = 7z

To find the domain of definition for this equation, we need to identify all values of the variables that would make the expression undefined. An expression becomes undefined when we have division by zero.

Let me first clarify the notation and rewrite the equation properly:
$\frac{\frac{24}{3t}+4}{24y+21\cdot2+6}=7z$

Now, let's identify where division by zero could occur:

Step 1: Analyze the numerator
The numerator is $\frac{24}{3t}+4$. For this to be defined, we need:
$3t \neq 0$
Therefore: $t \neq 0$

Step 2: Analyze the denominator
The denominator is $24y+21\cdot2+6$. Let's simplify this:
$24y + 42 + 6 = 24y + 48$

For the entire fraction to be defined, we need:
$24y + 48 \neq 0$
$24y \neq -48$
$y \neq -2$

Step 3: State the domain restrictions
For the equation to be defined, both conditions must be satisfied simultaneously:

• $t \neq 0$ (to avoid division by zero in the numerator)
• $y \neq -2$ (to avoid division by zero in the main denominator)

Therefore, the domain of definition is: $y \neq -2, t \neq 0$