Q. Simplify. Express your answer as a single fraction in simplest form. 4c5−32b
Identify LCD: Identify the least common denominator (LCD) for the fractions.The denominators are 4c and 3. The LCD for these two denominators is 12c because 12c is the smallest number that both 4c and 3 will divide into without a remainder.
Rewrite fractions: Rewrite each fraction with the common denominator of 12c. To convert the first fraction, 4c5, to have a denominator of 12c, multiply both the numerator and the denominator by 3. For the second fraction, 32b, multiply both the numerator and the denominator by 4c. (4c5)⋅(33)=12c15(32b)⋅(4c4c)=12c8bc
Combine fractions: Combine the fractions with the common denominator.Now that both fractions have the same denominator, you can combine them by subtracting the numerators and keeping the common denominator.(12c15)−(12c8bc)=12c15−8bc
Simplify expression: Simplify the expression, if possible.In this case, the numerator 15−8bc cannot be simplified further because there are no common factors between the terms. Therefore, the expression in simplest form is 12c15−8bc.
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