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Simplify. Write your answer using whole numbers and variables.\newlined2−3dd−3\frac{d^2 - 3d}{d - 3}

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Full solution

Q. Simplify. Write your answer using whole numbers and variables.\newlined2−3dd−3\frac{d^2 - 3d}{d - 3}
  1. Factorize numerator: Factor the numerator if possible.\newlineWe look for common factors in the terms of the numerator d2−3dd^2 - 3d. Both terms have a common factor of dd.\newlined2−3d=d(d−3)d^2 - 3d = d(d - 3)
  2. Cancel common factors: Simplify the expression by canceling out common factors.\newlineWe have the expression (d(d−3))/(d−3)(d(d - 3))/(d - 3). The (d−3)(d - 3) terms in the numerator and denominator cancel each other out because (d−3)/(d−3)=1(d - 3)/(d - 3) = 1.\newline(d(d−3))/(d−3)=d∗((d−3)/(d−3))=d∗1=d(d(d - 3))/(d - 3) = d * ((d - 3)/(d - 3)) = d * 1 = d
  3. Check variable restrictions: Check for any restrictions on the variable.\newlineWe must remember that the original denominator was (d−3)(d - 3), so dd cannot be equal to 33 because division by zero is undefined.

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