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Solve the equation. 7 X-4 X = 5 2x²5x- 12 X 1 2x + 3

Solve the equation. 7 X-4 X = 5 2x²5x- 12 X 1 2x + 3

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Solve the equation:** \[ \frac{7}{x - 4} - \frac{5}{2x^2 - 5x - 12} = \frac{1}{2x + 3} \] **Solution:** Here, we are given a rational equation with three fractions. To solve this equation, follow these steps: 1. **Find a common denominator:** Identify the least common denominator (LCD) for all three fractions on both sides of the equation. 2. **Eliminate fractions:** Multiply each term in the equation by the LCD to eliminate the fractions. 3. **Solve for \( x \):** Simplify the resulting equation and solve for the variable \( x \). 4. **Check for extraneous solutions:** Substitute the solutions back into the original equation to ensure they do not create any undefined expressions (such as division by zero). The image displays a placeholder to input the solution \( x = \) with a symbol indicating that the provided answer is incorrect. Make sure to check your calculations thoroughly.
Transcribed Image Text:**Solve the equation:** \[ \frac{7}{x - 4} - \frac{5}{2x^2 - 5x - 12} = \frac{1}{2x + 3} \] **Solution:** Here, we are given a rational equation with three fractions. To solve this equation, follow these steps: 1. **Find a common denominator:** Identify the least common denominator (LCD) for all three fractions on both sides of the equation. 2. **Eliminate fractions:** Multiply each term in the equation by the LCD to eliminate the fractions. 3. **Solve for \( x \):** Simplify the resulting equation and solve for the variable \( x \). 4. **Check for extraneous solutions:** Substitute the solutions back into the original equation to ensure they do not create any undefined expressions (such as division by zero). The image displays a placeholder to input the solution \( x = \) with a symbol indicating that the provided answer is incorrect. Make sure to check your calculations thoroughly.
Expert Solution
Step 1: The given equation is:

fraction numerator 7 over denominator x minus 4 end fraction minus fraction numerator 5 over denominator 2 x squared minus 5 x minus 12 end fraction equals fraction numerator 1 over denominator 2 x plus 3 end fraction

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