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Simplify. Express your answer as a single fraction in simplest form. \newline9st24+9t2\frac{9st^2}{4} + \frac{9t}{2}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline9st24+9t2\frac{9st^2}{4} + \frac{9t}{2}
  1. Find LCM of Denominators: Find the least common multiple (LCM) of the denominators 44 and 22. The LCM is 44.
  2. Make Denominators Same: Make the denominators the same by multiplying the second fraction by 22. This gives us (9st2)/4+(18t)/4(9st^2)/4 + (18t)/4.
  3. Add Numerators: Add the numerators since the denominators are the same. The combined fraction is (9st2+18t)/4(9st^2 + 18t)/4.
  4. Factor Out Common Factor: Check if the numerator can be simplified further. Both terms in the numerator have a common factor of 9t9t, so we can factor that out. This gives us 9t(st+2)4\frac{9t(st + 2)}{4}.
  5. Simplify Fraction: Check if there are any common factors between the numerator and the denominator that can be simplified. There are no common factors between 9t9t and 44, so the fraction is already in its simplest form.

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