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Simplify. Express your answer as a single fraction in simplest form. \newlinecc − -2c\frac{2}{c}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newlinecc − -2c\frac{2}{c}
  1. Identify expression: Identify the expression to be simplified.\newlineWe have the expression c−2cc - \frac{2}{c}. To combine these terms into a single fraction, we need a common denominator.
  2. Find common denominator: Find a common denominator.\newlineThe common denominator for cc and 2c\frac{2}{c} is cc. We can rewrite cc as c1\frac{c}{1} to make it easier to combine the fractions.
  3. Rewrite with common denominator: Rewrite the expression with the common denominator.\newlineWe rewrite cc as c1\frac{c}{1} and keep 2c\frac{2}{c} as it is. Now we have:\newlinec1\frac{c}{1} - 2c\frac{2}{c}
  4. Combine fractions: Combine the fractions.\newlineSince we have a common denominator, we can combine the numerators:\newline(c⋅c)/c−2/c(c \cdot c)/c - 2/c\newline=(c2)/c−2/c= (c^2)/c - 2/c
  5. Simplify combined fraction: Simplify the combined fraction. Now we subtract the numerators and keep the common denominator: (c2)−2c\frac{(c^2) - 2}{c}
  6. Check for further simplification: Check if the fraction can be simplified further.\newlineThe fraction (c2)−2c\frac{(c^2) - 2}{c} cannot be simplified further because c2−2c^2 - 2 does not have a factor of cc that can be canceled with the cc in the denominator.

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