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Simplify. Express your answer as a single fraction in simplest form. \newline7y3z544y4z5\frac{7y^3z^5}{4} - \frac{4y^4z}{5}

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline7y3z544y4z5\frac{7y^3z^5}{4} - \frac{4y^4z}{5}
  1. Identify Common Denominator: Identify the common denominator for the two fractions.\newlineSince the fractions have different denominators (44 and 55), we need to find the least common multiple (LCM) of these two numbers to combine the fractions. The LCM of 44 and 55 is 2020.
  2. Rewrite with Common Denominator: Rewrite each fraction with the common denominator of 2020. To convert the first fraction's denominator from 44 to 2020, we multiply both the numerator and the denominator by 55. For the second fraction, we multiply both the numerator and the denominator by 44. 7y3z54×554y4z5×44\frac{7y^3z^5}{4} \times \frac{5}{5} - \frac{4y^4z}{5} \times \frac{4}{4} =7y3z5×54×54y4z×45×4\frac{7y^3z^5 \times 5}{4 \times 5} - \frac{4y^4z \times 4}{5 \times 4} =35y3z52016y4z20\frac{35y^3z^5}{20} - \frac{16y^4z}{20}
  3. Combine Fractions: Combine the fractions over the common denominator.\newlineNow that both fractions have the same denominator, we can combine them into a single fraction.\newline=35y3z516y4z20=\frac{35y^3z^5 - 16y^4z}{20}
  4. Simplify Numerator: Simplify the numerator if possible.\newlineIn this case, the terms in the numerator do not have common factors (other than 11) and cannot be combined further because they have different powers of yy and zz. Therefore, the expression is already in its simplest form.

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