Q. Simplify. Express your answer as a single fraction in simplest form. 47y3z5−54y4z
Identify Common Denominator: Identify the common denominator for the two fractions.Since the fractions have different denominators (4 and 5), we need to find the least common multiple (LCM) of these two numbers to combine the fractions. The LCM of 4 and 5 is 20.
Rewrite with Common Denominator: Rewrite each fraction with the common denominator of 20. To convert the first fraction's denominator from 4 to 20, we multiply both the numerator and the denominator by 5. For the second fraction, we multiply both the numerator and the denominator by 4. 47y3z5×55−54y4z×44 =4×57y3z5×5−5×44y4z×4 =2035y3z5−2016y4z
Combine Fractions: Combine the fractions over the common denominator.Now that both fractions have the same denominator, we can combine them into a single fraction.=2035y3z5−16y4z
Simplify Numerator: Simplify the numerator if possible.In this case, the terms in the numerator do not have common factors (other than 1) and cannot be combined further because they have different powers of y and z. Therefore, the expression is already in its simplest form.
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