Q. Multiply. Write your answer in simplest form.5g−34g2+g−5×4g+55g−3
Identify Expressions: Identify the expressions to be multiplied.We have two fractions to multiply: (4g2+g−5)/(5g−3) and (5g−3)/(4g+5).
Multiply Numerators and Denominators: Multiply the numerators and the denominators of the fractions.The multiplication of the fractions is done by multiplying the numerators together and the denominators together:(4g2+g−5)×(5g−3)/((5g−3)×(4g+5)).
Find Common Factors: Look for common factors in the numerator and the denominator.We notice that (5g−3) is a common factor in both the numerator and the denominator, which means we can cancel it out.
Cancel Common Factors: Cancel the common factors.After canceling (5g−3) from the numerator and the denominator, we are left with:(4g2+g−5)/(4g+5).
Check for Further Simplification: Check if the remaining expression can be simplified further.The remaining expression (4g2+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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