(x-7)%2F(x-5)(x%2B4)%3D1-verify.jpeg "(2+x)(x-7)/(x-5)(x+4)=1 Verify")
Verifying the Equation: (2+x)(x-7)/(x-5)(x+4) = 1
This article will guide you through the process of verifying whether the equation (2+x)(x-7)/(x-5)(x+4) = 1 is true. We will explore the steps involved in solving the equation and determine if the equation holds true for all values of x.
Understanding the Equation
The equation involves rational expressions, where both sides contain fractions with variables in the numerator and denominator. To verify if the equation is true, we need to manipulate the expressions to determine if they are equivalent.
Solving the Equation
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Cross-Multiplication: Begin by cross-multiplying the equation to eliminate the fractions. This gives us: (2+x)(x-7) = (x-5)(x+4)
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Expanding: Expand both sides of the equation by multiplying out the brackets: 2x - 14 + x² - 7x = x² - x - 20
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Simplifying: Combine like terms on both sides of the equation: -5x - 14 = -x - 20
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Solving for x: Isolate the variable x by adding 5x and 20 to both sides of the equation: 6 = 4x
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Final Step: Divide both sides by 4 to get the value of x: x = 3/2
Analysis
By solving the equation, we found that the equation holds true only for x = 3/2. This means the equation is not universally true for all values of x. It's only true for a specific value of x.
Conclusion
Therefore, we can conclude that the equation (2+x)(x-7)/(x-5)(x+4) = 1 is not true for all values of x. It holds true only for x = 3/2. Remember, verifying equations involving rational expressions often requires careful manipulation and attention to potential restrictions on the values of the variables.