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Multiply. Write your answer in simplest form.\newline4g2+g55g3×5g34g+5\frac{4g^2 + g - 5}{5g - 3} \times \frac{5g - 3}{4g + 5}

Full solution

Q. Multiply. Write your answer in simplest form.\newline4g2+g55g3×5g34g+5\frac{4g^2 + g - 5}{5g - 3} \times \frac{5g - 3}{4g + 5}
  1. Identify Expressions: Identify the expressions to be multiplied.\newlineWe have two fractions to multiply: (4g2+g5)/(5g3)(4g^2 + g - 5)/(5g - 3) and (5g3)/(4g+5)(5g - 3)/(4g + 5).
  2. Multiply Numerators and Denominators: Multiply the numerators and the denominators of the fractions.\newlineThe multiplication of the fractions is done by multiplying the numerators together and the denominators together:\newline(4g2+g5)×(5g3)/((5g3)×(4g+5))(4g^2 + g - 5) \times (5g - 3) / ((5g - 3) \times (4g + 5)).
  3. Find Common Factors: Look for common factors in the numerator and the denominator.\newlineWe notice that (5g3)(5g - 3) is a common factor in both the numerator and the denominator, which means we can cancel it out.
  4. Cancel Common Factors: Cancel the common factors.\newlineAfter canceling (5g3)(5g - 3) from the numerator and the denominator, we are left with:\newline(4g2+g5)/(4g+5)(4g^2 + g - 5) / (4g + 5).
  5. Check for Further Simplification: Check if the remaining expression can be simplified further.\newlineThe remaining expression (4g2+g5)/(4g+5)(4g^2 + g - 5) / (4g + 5) does not have any common factors, and the numerator cannot be factored to cancel out with the denominator. Therefore, this is the simplest form.

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