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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 87
Chapter 1, Problem 87

Perform each division. See Examples 7 and 8. (8wxy2+3wx2y+12w2xy)/(4wx2y)(8wxy^2+3wx^2y+12w^2xy)/(4wx^2y)

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Identify the division problem: \(\frac{8wxy^{2} + 3wx^{2}y + 12w^{2}xy}{4wx^{2}y}\).
Rewrite the expression as the sum of three separate fractions: \(\frac{8wxy^{2}}{4wx^{2}y} + \frac{3wx^{2}y}{4wx^{2}y} + \frac{12w^{2}xy}{4wx^{2}y}\).
Simplify each fraction individually by canceling common factors in the numerator and denominator:
- For \(\frac{8wxy^{2}}{4wx^{2}y}\), cancel common variables and coefficients.
- For \(\frac{3wx^{2}y}{4wx^{2}y}\), cancel common variables and coefficients.
- For \(\frac{12w^{2}xy}{4wx^{2}y}\), cancel common variables and coefficients.
After simplifying each term, combine the results to write the final simplified expression.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Polynomial Division

Polynomial division involves dividing one polynomial by another, similar to numerical division. Each term in the numerator is divided by the denominator, simplifying the expression step-by-step. Understanding how to divide terms with variables and exponents is essential.
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Introduction to Polynomials

Laws of Exponents

The laws of exponents govern how to handle powers when multiplying, dividing, or raising powers to powers. For division, subtract the exponents of like bases. This is crucial when simplifying terms like w^a / w^b or x^a / x^b in the expression.
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Rational Exponents

Combining Like Terms

After dividing each term, combining like terms means adding or subtracting terms with the same variables raised to the same powers. This step simplifies the expression to its simplest form, making it easier to interpret or use in further calculations.
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Combinations
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