Question

Simplify each expression. $$ \frac{x-\frac{x}{2}}{x+\frac{x}{8}} $$

   Simplify each expression.
$$
\frac{x-\frac{x}{2}}{x+\frac{x}{8}}
$$

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 8, Problem 16

Instant Answer

Solved by Expert Ashley High

03/18/2020

Step 1

We can do this by multiplying the numerator and denominator of the first fraction by 2 and the numerator and denominator of the second fraction by 8. This gives us: $$ \frac{2x-\frac{x}{2}\times2}{2x+\frac{x}{8}\times8} $$ Show more…

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Simplify each expression. $$ \frac{x-\frac{x}{2}}{x+\frac{x}{8}} $$

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Key Concepts

Canceling Common Factors

This involves identifying and removing alike factors that appear in both the numerator and denominator in a fraction, which simplifies the expression further and reduces its complexity.

Simplifying Algebraic Expressions

This concept involves rewriting expressions to a more compact or reduced form by combining like terms, reducing fractions, and eliminating redundancies. It is essential for making problems easier to solve and understand in algebra.

Complex Fractions

Complex fractions are fractions in which the numerator, denominator, or both contain additional fractional expressions. Simplifying them typically requires combining inner fractions by finding common denominators or multiplying by the reciprocal, thereby transforming the expression into a simpler single fraction.

Common Denominator

When adding or subtracting fractions within an expression, a common denominator must be found. This process allows the fractions to be combined into a single term, leading to a more straightforward simplification of the overall expression.

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