Evaluate the Algebraic Fraction: (a-bc)/(b·-c) = 0

Indicate whether true or false

$\frac{a-b\operatorname{\cdot}c}{b\operatorname{\cdot}-c}=0$

To solve this problem, we will follow these steps:

• Step 1: Analyze the numerator $a - b \cdot c$.
• Step 2: Analyze the denominator $b \cdot -c$.
• Step 3: Determine conditions for the fraction to be zero.

Now, let's work through each step:
Step 1: The numerator is $a - b \cdot c$. This becomes zero if $a = b \cdot c$.
Step 2: The denominator is $b \cdot -c = -(b \cdot c)$. This simplifies to the negative of the product $b \cdot c$.
Step 3: For the expression $\frac{a-b \cdot c}{b \cdot -c}$ to equal zero, the numerator must be zero, i.e., $a = b \cdot c$, but the denominator must not be zero. However, if $a = b \cdot c$, then the denominator becomes zero because it’s negative of the same product, $-(b \cdot c)$, creating an undefined scenario rather than zero.

Since making the numerator zero results in the denominator being undefined, the expression cannot be zero. Therefore, the statement is Not true.