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(3x+10)/(x^(2)+9x+20)

22) 3x+10x2+9x+20 \frac{3 x+10}{x^{2}+9 x+20}

Full solution

Q. 22) 3x+10x2+9x+20 \frac{3 x+10}{x^{2}+9 x+20}
  1. Identify Expression: Identify the expression to be simplified.\newlineThe expression given is (3x+10)/(x2+9x+20)(3x+10)/(x^2+9x+20).
  2. Factor Denominator: Factor the denominator.\newlineThe denominator x2+9x+20x^2+9x+20 can be factored into (x+5)(x+4)(x+5)(x+4).
  3. Check Factors: Check if the numerator can be factored or if there are common factors with the denominator.\newlineThe numerator 3x+103x+10 cannot be factored in a way that will cancel out with the factors of the denominator.
  4. Write Simplified Expression: Write the simplified expression.\newlineSince there are no common factors between the numerator and the denominator, the expression is already in its simplest form.

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