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Simplify. Express your answer as a single fraction in simplest form. \newline9y2+49yz\frac{9y}{2} + \frac{4}{9yz}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline9y2+49yz\frac{9y}{2} + \frac{4}{9yz}
  1. Find LCM: Find the least common multiple (LCM) of the denominators 22 and 9yz9yz. Since 22 and 9yz9yz have no common factors other than 11, the LCM is simply their product, which is 18yz18yz.
  2. Make denominators same: Make the denominators the same by multiplying the first fraction by 9yz9yz and the second fraction by 22. This gives us (9y×9yz)/(2×9yz)+(4×2)/(9yz×2)(9y \times 9yz) / (2 \times 9yz) + (4 \times 2) / (9yz \times 2).
  3. Perform multiplications: Perform the multiplications in the numerators and denominators. This results in (81y2z)/(18yz)+(8)/(18yz)(81y^2z) / (18yz) + (8) / (18yz).
  4. Combine fractions: Combine the fractions over the common denominator. The combined fraction is (81y2z+818yz)(\frac{81y^2z + 8}{18yz}).
  5. Simplify fraction: Simplify the fraction if possible. In this case, there are no common factors between the numerator and the denominator that can be canceled out, so the fraction is already in its simplest form.

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