Textbook Question
In Exercises 15–32, multiply or divide as indicated. (x3−25x)/4x2 ⋅ (2x2−2)/(x2−6x+5) ÷ (x2+5x)/(7x+7)
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0. Review of Algebra
Polynomials Intro
2:39 minutesProblem 37
Textbook Question
Add or subtract as indicated. (4x−10)/(x−2) − (x−4)/(x−2)
Verified step by step guidance1
Identify that both rational expressions have the same denominator, which is \(x - 2\).
Since the denominators are the same, combine the numerators by subtracting: \((4x - 10) - (x - 4)\).
Distribute the subtraction across the second numerator: \$4x - 10 - x + 4$.
Combine like terms in the numerator: \((4x - x) + (-10 + 4)\).
Write the simplified numerator over the common denominator: \(\frac{3x - 6}{x - 2}\).
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Like Denominators in Rational Expressions
When adding or subtracting rational expressions, the denominators must be the same. If the denominators are identical, you can combine the numerators directly while keeping the denominator unchanged. This simplifies the process and avoids the need for finding a common denominator.
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Rationalizing Denominators
Combining Numerators
After confirming the denominators are the same, subtract or add the numerators as indicated. This involves combining like terms carefully to simplify the resulting expression. Proper handling of subtraction signs is crucial to avoid errors.
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Simplifying Rational Expressions
Once the numerators are combined, simplify the resulting rational expression by factoring and reducing common factors if possible. Simplification makes the expression easier to interpret and use in further calculations.
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