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Simplify. Express your answer as a single fraction in simplest form. \newline6y55+56y5z\frac{6y^5}{5} + \frac{5}{6y^5z}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline6y55+56y5z\frac{6y^5}{5} + \frac{5}{6y^5z}
  1. Identify common denominator: Identify the common denominator for the two fractions.\newlineThe common denominator for the fractions 6y55\frac{6y^5}{5} and 56y5z\frac{5}{6y^5z} is 5×6y5z5 \times 6y^5z.
  2. Rewrite with common denominator: Rewrite each fraction with the common denominator.\newlineThe first fraction becomes (6y55)⋅(6z6z)=36y5z30y5z(\frac{6y^5}{5}) \cdot (\frac{6z}{6z}) = \frac{36y^5z}{30y^5z}.\newlineThe second fraction becomes (56y5z)⋅(55)=2530y5z(\frac{5}{6y^5z}) \cdot (\frac{5}{5}) = \frac{25}{30y^5z}.
  3. Combine fractions: Combine the fractions over the common denominator. 36y5z+2530y5z\frac{36y^5z + 25}{30y^5z}
  4. Simplify fraction: Simplify the fraction if possible.\newlineThe numerator and the denominator do not have common factors other than 11, so the fraction is already in its simplest form.

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