Simplify. Express your answer as a single fraction in simplest form. \[ 2-\frac{b}{b+5} \]
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To simplify the expression \( 2 - \frac{b}{b+5} \), we start by expressing the number 2 as a fraction with the same denominator: \[ 2 = \frac{2(b+5)}{b+5} = \frac{2b + 10}{b + 5} \] Now, we can substitute this back into the original expression: \[ 2 - \frac{b}{b + 5} = \frac{2b + 10}{b + 5} - \frac{b}{b + 5} \] Since both fractions have the same denominator, we can combine them: \[ = \frac{(2b + 10) - b}{b + 5} \] Now, simplifying the numerator: \[ = \frac{2b + 10 - b}{b + 5} = \frac{b + 10}{b + 5} \] The expression \(\frac{b + 10}{b + 5}\) is already in simplest form. Therefore, the final answer is: \[ \boxed{\frac{b + 10}{b + 5}} \]
