Evaluate (x^2 - 25) / (x^2 + 25) when x = 2.
Understand the Problem
The question asks us to evaluate the expression (x^2 - 25) / (x^2 + 25) when x = 2. This involves substituting the value of x into the expression and then simplifying.
Answer
$-\frac{21}{29}$
Answer for screen readers
$ -\frac{21}{29} $
Steps to Solve
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Substitute $x = 2$ into the expression Replace $x$ with $2$ in the expression $\frac{x^2 - 25}{x^2 + 25}$: $$ \frac{2^2 - 25}{2^2 + 25} $$
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Evaluate the squares Calculate $2^2$: $2^2 = 4$ Substitute this value back into the expression: $$ \frac{4 - 25}{4 + 25} $$
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Perform the subtractions and additions Calculate the numerator: $4 - 25 = -21$ Calculate the denominator: $4 + 25 = 29$ So the expression becomes: $$ \frac{-21}{29} $$
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Simplify the fraction (if possible) The fraction $\frac{-21}{29}$ is already in its simplest form because 21 and 29 do not share any common factors other than 1. We can also write the fraction as $-\frac{21}{29}$.
$ -\frac{21}{29} $
More Information
The result is a negative fraction because the numerator is negative and the denominator is positive.
Tips
A common mistake is to incorrectly evaluate $2^2$ as something other than 4. Another common mistake is to incorrectly perform the addition or subtraction in either the numerator or denominator. Finally, always make sure the fraction is simplified completely.
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