Problem 62 Evaluate. If an expression is un... [FREE SOLUTION]

Chapter 1: Problem 62

Evaluate. If an expression is undefined, say so. $$\frac{-6-2(-3)}{8-3(-3)}$$

Short Answer

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Step by step solution

Simplify the numerator

Evaluate the numerator expression $-6 - 2(-3)$. First, handle the multiplication inside the parentheses. $-2 \times -3 = 6$. The numerator becomes: $-6 + 6 = 0$.

Simplify the denominator

Evaluate the denominator expression $8 - 3(-3)$. First, handle the multiplication inside the parentheses. $ -3 \times -3 = 9$. The denominator becomes: $8 + 9 = 17$.

Simplify the entire expression

Now that we have simplified both the numerator and the denominator, the expression becomes $\frac{0}{17}$. Since the numerator is zero, the overall value of the expression is \0\.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions

In mathematics, simplifying expressions means making them easier to understand or solve. Usually, you simplify by combining like terms and performing operations within parentheses first.
In our exercise, you notice we first simplified individual parts of the numerator and denominator.
For instance, in the numerator we had `-6 - 2(-3)`. According to math rules, you perform multiplication before addition and subtraction.
We calculated `-2 脳 -3 = 6` and then combined terms to get `-6 + 6 = 0`.

Numerator and Denominator

Rational expressions consist of a numerator (top part) and a denominator (bottom part).
In our problem, the numerator was `-6 - 2(-3)` and the denominator was `8 - 3(-3)`.
We needed to simplify both parts individually before solving the fraction.
Understanding each part separately helps simplify the overall expression.
Calculating the simplified numerator resulted in `-6 - (-6) = 0`, while the simplified denominator is `8 + 9 = 17`.
Therefore, we get the expression $\frac{0}{17}$.

Undefined Expressions

An expression becomes undefined when certain operations make it impossible to provide a meaningful result.
One common occurrence of undefined expressions in rational expressions is when the denominator is zero.
Dividing by zero is not allowed in mathematics as it leads to contradictions and undefined meanings.
In our given problem, the denominator was `17` after simplification.
Since `17` is not zero, our expression is defined and evaluates to `0`.
Always check whether the denominator is zero after simplification to determine if an expression is undefined.

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91影视

Evaluate. If an expression is undefined, say so. $$\frac{-6-2(-3)}{8-3(-3)}$$

Short Answer

Step by step solution

Simplify the numerator

Simplify the denominator

Simplify the entire expression

Key Concepts

Simplifying Expressions

Numerator and Denominator

Undefined Expressions

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