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Simplify. Express your answer as a single fraction in simplest form. \newlinec43+6\frac{c^4}{3} + 6

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Q. Simplify. Express your answer as a single fraction in simplest form. \newlinec43+6\frac{c^4}{3} + 6
  1. Identify Given Expression: Identify the given expression and the common denominator needed to combine the terms into a single fraction.\newlineThe given expression is c4/3+6c^4/3 + 6. To combine these terms into a single fraction, we need a common denominator. Since 66 is a whole number, we can express it as a fraction with the same denominator as the first term, which is 33. So, we rewrite 66 as 6/16/1 and then find a common denominator.
  2. Convert Whole Number to Fraction: Convert the whole number to a fraction with the common denominator.\newlineTo convert 66 to a fraction with the denominator 33, we multiply both the numerator and the denominator by 33. This gives us 6×3/1×36 \times 3 / 1 \times 3, which simplifies to 18/318/3.
  3. Combine Fractions with Common Denominator: Combine the two fractions with the common denominator.\newlineNow we have c43+183\frac{c^4}{3} + \frac{18}{3}. Since they have the same denominator, we can combine the numerators and keep the common denominator. This gives us c4+183\frac{c^4 + 18}{3}.
  4. Check for Further Simplification: Check if the resulting fraction can be simplified further.\newlineThe fraction (c4+18)/3(c^4 + 18)/3 cannot be simplified further because c4c^4 and 1818 do not have any common factors other than 11, and 33 does not factor into 1818 more than once. Therefore, the fraction is already in its simplest form.

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