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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form. (60x^(3))/(72x^(2)) Answer:

Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.\newline60x372x2 \frac{60 x^{3}}{72 x^{2}} \newlineAnswer:

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.\newline60x372x2 \frac{60 x^{3}}{72 x^{2}} \newlineAnswer:
  1. Factor out GCD: Factor out the greatest common divisor from the numerator and the denominator.\newlineThe greatest common divisor of 6060 and 7272 is 1212. We can also simplify x3/x2x^{3}/x^{2} by subtracting the exponents.\newline(60x3)/(72x2)=(12⋅5⋅x3)/(12⋅6⋅x2)(60x^{3})/(72x^{2}) = (12\cdot 5\cdot x^{3})/(12\cdot 6\cdot x^{2})
  2. Cancel common factors: Cancel out the common factors.\newlineThe 1212 in the numerator and denominator cancels out, as does x2x^{2} because x3/x2=x3−2=xx^{3}/x^{2} = x^{3-2} = x.\newline(12⋅5⋅x3)/(12⋅6⋅x2)=(5⋅x)/(6)(12\cdot 5\cdot x^{3})/(12\cdot 6\cdot x^{2}) = (5\cdot x)/(6)
  3. Check for further simplification: Check if the fraction can be simplified further.\newlineThe fraction (5×x)/(6)(5\times x)/(6) cannot be simplified further because 55 and 66 have no common factors other than 11, and xx is already in its simplest form.

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