Q. Simplify. Express your answer as a single fraction in simplest form. bc42+c4
Identify LCM: Identify the least common multiple (LCM) of the denominators bc4 and c. Since c is a factor of bc4, the LCM is bc4.
Rewrite fractions: Rewrite each fraction with the LCM as the denominator. To do this, multiply the numerator and denominator of the first fraction by c and the numerator and denominator of the second fraction by b4c3. This gives us (2c)/(bc4)+(4b4c3)/(bc4).
Simplify numerators: Simplify the numerators of both fractions. The first fraction remains unchanged as (2c)/(bc4). The second fraction simplifies to (4b4c3)/(bc4) because b4c3 is the result of multiplying 4 by b4c3.
Combine fractions: Combine the fractions now that they have the same denominator. This results in (2c+4b4c3)/(bc4).
Factor out common factor: Factor out the common factor of c from the numerator. This gives us bc4c(2+4b4c2).
Cancel common factor: Simplify the fraction by canceling out the common factor of c from the numerator and denominator. This results in (2+4b4c2)/(b1c3).
Write final answer: Write the final simplified expression. The final answer is (2+4b4c2)/(bc3).
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