Question

Simplify. Show your steps. $$\frac{9^{2}-21}{56-2(4+1)^{2}}$$

   Simplify. Show your steps.
$$\frac{9^{2}-21}{56-2(4+1)^{2}}$$

Prealgebra

Tom Carson 4th Edition

Chapter 1, Problem 41

Instant Answer

Solved by Expert Ali Soave

05/14/2020

Step 1

$$\frac{9^{2}-21}{56-2(4+1)^{2}} = \frac{9^{2}-21}{56-2(5)^{2}}$$ Show more…

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Simplify. Show your steps. $$\frac{9^{2}-21}{56-2(4+1)^{2}}$$

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Key Concepts

Simplifying Rational Expressions

This involves simplifying expressions that are in the form of a fraction, where both the numerator and the denominator are simplified independently before combining them. Understanding how to work with both parts of the fraction using the correct arithmetic and algebraic rules is key to correctly simplifying the overall expression.

Order of Operations

This concept refers to the rules that determine the sequence in which operations should be carried out in a mathematical expression. These rules, often remembered by acronyms like PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction), ensure that expressions are interpreted and simplified consistently.

Exponentiation

Exponentiation is the mathematical operation involving the raising of a base to a power. It is important to perform exponentiation as specified before carrying out multiplication or other operations, which is why knowing how to correctly compute and simplify terms with exponents is crucial.

Arithmetic Simplification

Arithmetic simplification involves applying basic operations such as addition, subtraction, multiplication, and division in a systematic way to reduce an expression to its simplest form. This also includes combining like terms and reducing fractions, ensuring the final answer is as concise as possible.

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