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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form. (40x^(3))/(12x^(4)) Answer:

Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.\newline40x312x4 \frac{40 x^{3}}{12 x^{4}} \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.\newline40x312x4 \frac{40 x^{3}}{12 x^{4}} \newlineAnswer:
  1. Factor out common factor: Factor out the greatest common factor from the numerator and the denominator.\newlineThe greatest common factor of 4040 and 1212 is 44, and the smallest power of xx that appears in both the numerator and the denominator is x3x^{3}.\newlineSo, we can factor out 4x34x^{3} from both the numerator and the denominator.\newline40x312x4=4x3⋅104x3⋅3\frac{40x^{3}}{12x^{4}} = \frac{4x^{3} \cdot 10}{4x^{3} \cdot 3}
  2. Cancel common factors: Cancel out the common factors from the numerator and the denominator.\newlineThe 4x34x^{3} in the numerator and the denominator cancel each other out.\newline4x3×104x3×3=103\frac{4x^{3} \times 10}{4x^{3} \times 3} = \frac{10}{3}
  3. Cancel x3x^3: Since x3x^{3} is in both the numerator and the denominator, we can also cancel out x3x^{3}. This leaves us with x3x^{3} in the denominator, which is x4−3=x1x^{4 - 3} = x^{1} or simply xx. 103x\frac{10}{3x}
  4. Check for simplifications: Check for any remaining simplifications. There are no more common factors, and the expression is as simple as it can be.

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