1Cademy - Explain the steps to add and simplify: $$\frac{7x+12}{x+3} + \frac{x^2}{x+3}$$.

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Adding $\frac{7x+12}{x+3} + \frac{x^2}{x+3}$

Essay

Explain the steps to add and simplify: $\frac{7x+12}{x+3} + \frac{x^2}{x+3}$ .

Question: Explain the steps to add and simplify: $\frac{7x+12}{x+3} + \frac{x^2}{x+3}$ .

Sample answer: First, add the numerators over the common denominator to get $\frac{x^2 + 7x + 12}{x + 3}$ . Next, factor the numerator to $(x + 3)(x + 4)$ . Finally, cancel the common factor of $(x + 3)$ to get the answer, $x + 4$ .

Key points:

Combine the numerators over the common denominator to get $\frac{x^2 + 7x + 12}{x + 3}$ .
Factor the numerator $x^2 + 7x + 12$ into $(x + 3)(x + 4)$ .
Cancel the common factor $(x + 3)$ to simplify the expression to $x + 4$ .

Rubric: The answer should describe adding the numerators, factoring the resulting trinomial, and canceling the common factor to arrive at the simplified expression.

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Updated 2026-06-20

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