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Difficulty: MediumEvaluating Algebraic Expressions
Find the numerical value of the rational expression 3a2−4bc+2\frac{3a^2 - 4b}{c + 2} using the parameter values a=−2a = -2, b=−5b = -5, and c=−6c = -6.

Answer: -8

Answer

The final numerical value is -8.
The correct value is found by carefully substituting the negative integer values into the rational expression, strictly applying the order of operations (exponents, then multiplication, then addition/subtraction), and accurately tracking the signs at each step to get 32 in the numerator and -4 in the denominator, which yields -8.

Step-by-Step Solution

1
Substitute the given values into the expression.
3(−2)2−4(−5)−6+2\frac{3(-2)^2 - 4(-5)}{-6 + 2}
Replace variables aa, bb, and cc with their assigned numerical equivalents to begin evaluation.
2
Evaluate the exponent in the numerator.
3(4)−4(−5)−6+2\frac{3(4) - 4(-5)}{-6 + 2}
According to the order of operations, exponents must be evaluated before multiplication. The square of a negative number is positive: (−2)2=4(-2)^2 = 4.
3
Perform the multiplications in the numerator.
12−(−20)−6+2\frac{12 - (-20)}{-6 + 2}
Calculate the products: 3×4=123 \times 4 = 12 and 4×(−5)=−204 \times (-5) = -20.
4
Simplify the subtraction in the numerator.
12+20−6+2=32−6+2\frac{12 + 20}{-6 + 2} = \frac{32}{-6 + 2}
Subtracting a negative number is equivalent to adding a positive number: 12−(−20)=12+20=3212 - (-20) = 12 + 20 = 32.
5
Evaluate the addition in the denominator.
32−4\frac{32}{-4}
Combine the constant terms in the denominator: −6+2=−4-6 + 2 = -4.
6
Divide the numerator by the denominator.
-8
A positive number divided by a negative number results in a negative quotient: 32÷(−4)=−832 \div (-4) = -8.

Key Concept

Evaluating Algebraic Expressions
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Topics

Evaluating Algebraic Expressions

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