Mathematics

Mathematics

Problem

Evaluate (7c−9d)(d−c)5c2−3cd+d2\frac{(7c-9d)(d-c)}{5c^2-3cd+d^2} if c=2c = 2 and d=−4d = -4.
Intuitive explanation

The key is to recognize that direct substitution can be messy with nested operations—instead, try factoring the denominator first to see if it shares a common factor with the numerator. Once you simplify the expression algebraically, plugging in c=2c = 2 and d=−4d = -4 becomes straightforward arithmetic rather than a computational nightmare.

Intuitive explanation

The key is to recognize that direct substitution can be messy with nested operations—instead, try factoring the denominator first to see if it shares a common factor with the numerator. Once you simplify the expression algebraically, plugging in c=2c = 2 and d=−4d = -4 becomes straightforward arithmetic rather than a computational nightmare.

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