Domanda del libro di testo
Find the value of the objective function z = 2x + 3y at each corner of the graphed region shown. What is the maximum value of the objective function? What is the minimum value of the objective function?
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Ch. 5 - Systems of Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 6, Problema 57
Exercises 57–59 will help you prepare for the material covered in the next section. Subtract:
Guida verificata passo dopo passo1
Identify the two rational expressions to subtract: \(\frac{3}{x-4}\) and \(\frac{2}{x+2}\).
Find the least common denominator (LCD) of the two fractions. Since the denominators are \((x-4)\) and \((x+2)\), the LCD is the product of these two distinct factors: \((x-4)(x+2)\).
Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator appropriately:
- For \(\frac{3}{x-4}\), multiply numerator and denominator by \((x+2)\) to get \(\frac{3(x+2)}{(x-4)(x+2)}\).
- For \(\frac{2}{x+2}\), multiply numerator and denominator by \((x-4)\) to get \(\frac{2(x-4)}{(x-4)(x+2)}\).
Now that both fractions have the same denominator, subtract the numerators:
\(\frac{3(x+2) - 2(x-4)}{(x-4)(x+2)}\).
Simplify the numerator by distributing and combining like terms, then write the final expression as a single simplified rational expression.
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Finding a Common Denominator
When subtracting rational expressions, you must first find a common denominator. This involves identifying the least common denominator (LCD) that both denominators share, which allows you to rewrite each fraction with the same denominator for easy subtraction.
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02:58
Rationalizing Denominators
Subtracting Rational Expressions
After expressing both fractions with a common denominator, subtract the numerators while keeping the denominator the same. This step combines the expressions into a single rational expression, simplifying the subtraction process.
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02:58Rationalizing Denominators
Simplifying the Resulting Expression
Once the subtraction is performed, simplify the resulting rational expression by factoring and reducing common factors in the numerator and denominator. This ensures the expression is in its simplest form for clarity and further use.
Video consigliato:
05:07Simplifying Algebraic Expressions
Pratica correlata
Domanda del libro di testo
In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.
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Domanda del libro di testo
In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.
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Domanda del libro di testo
Find the length and width of a rectangle whose perimeter is 36 feet and whose area is 77 square feet.
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Exercises 57–59 will help you prepare for the material covered in the next section. Add: (5x−3)/(x2+1) + 2x/(x2+1)2.
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Domanda del libro di testo
Find the length and width of a rectangle whose perimeter is 40 feet and whose area is 96 square feet.
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