Question

$\frac{2 z^{2}}{4 z-1}-\frac{z-2 z^{2}}{4 z-1}$

   $\frac{2 z^{2}}{4 z-1}-\frac{z-2 z^{2}}{4 z-1}$

Algebra A Combined Function

Algebra A Combined Function

Elayn Martin-Gay 4th Edition

Chapter 7, Problem 64

Instant Answer

Solved by Expert Victor Salazar

02/07/2022

Step 1

This gives us: \[\frac{2z^{2} - (z - 2z^{2})}{4z - 1}\] Show more…

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$\frac{2 z^{2}}{4 z-1}-\frac{z-2 z^{2}}{4 z-1}$

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Key Concepts

Common Denominator

A common denominator is used when adding or subtracting rational expressions. Ensuring that the denominators are the same allows for the direct combination of the numerators, making the simplification process more straightforward.

Combining Like Terms

Combining like terms is an algebraic technique where terms with the same variables and exponents are added or subtracted. This process simplifies expressions by reducing the total number of terms, which is especially useful after merging expressions over a common denominator.

Rational Expressions

Rational expressions are fractions where both the numerator and the denominator are algebraic expressions, typically polynomials. Mastering these expressions involves simplifying, factoring, and performing arithmetic operations with them, which is key to solving many algebraic problems.

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