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Simplify. Write your answer using whole numbers and variables.\newline36c274c3\frac{36c - 27}{4c - 3}

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Q. Simplify. Write your answer using whole numbers and variables.\newline36c274c3\frac{36c - 27}{4c - 3}
  1. Identify Terms and Factors: Identify the terms in the expression and look for common factors. The expression is 36c274c336c - \frac{27}{4}c - 3. We can see that 36c36c and 274c-\frac{27}{4}c have a common variable cc.
  2. Factor Out Common Variable: Factor out the common variable cc from the terms 36c36c and 274c-\frac{27}{4}c. We can write the expression as c(36274)3c(36 - \frac{27}{4}) - 3.
  3. Simplify Inside Parentheses: Simplify the expression inside the parentheses.\newlineTo subtract 274\frac{27}{4} from 3636, we need to have a common denominator. The number 3636 can be written as 1444\frac{144}{4} to have the same denominator as 274\frac{27}{4}.\newlineSo, c(36274)c(36 - \frac{27}{4}) becomes c(1444274)c(\frac{144}{4} - \frac{27}{4}).
  4. Subtract Fractions: Subtract the fractions inside the parentheses.\newlinec(1444274)=c(1174)c\left(\frac{144}{4} - \frac{27}{4}\right) = c\left(\frac{117}{4}\right).
  5. Distribute Variable: Distribute the variable cc across the fraction.c(1174)=117c4.c\left(\frac{117}{4}\right) = \frac{117c}{4}.
  6. Combine Terms: Combine the term with the variable cc with the constant term 3-3. Since 3-3 does not have the same denominator as rac{117c}{4}, we need to write 3-3 with a denominator of 44 to combine them. 3-3 can be written as - rac{12}{4}. So, the expression becomes rac{117c}{4} - rac{12}{4}.
  7. Subtract Constants: Subtract the constant terms.\newline117c4124=117c124\frac{117c}{4} - \frac{12}{4} = \frac{117c - 12}{4}.
  8. Check for Simplification: Check if the numerator can be simplified further.\newlineThe numerator 117c12117c - 12 does not have any common factors with the denominator 44, so it cannot be simplified further.

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