Algebra

x^2 + 5x + 6)/(x + 2) = 4

Step-by-step solution with explanation

Final Answer

x = 2

Step-by-step solution

1

Factor the numerator completely

We look for two numbers that multiply to 6 and add to 5. Those numbers are 2 and 3. So we factor the quadratic into two binomials.
4

Solve the simple linear equation

Subtract 3 from both sides to isolate x. The solution is x = 2.

Understanding this problem

Learning Insight

Factoring lets you simplify a rational equation by canceling matching factors — turning a complex fraction into a simple linear equation. Always check your answer by plugging it back in, because algebra steps can hide small arithmetic slips.

Quick Tip

After canceling factors, the equation becomes linear (degree 1), so it has exactly one solution. Always verify by substituting back into the ORIGINAL equation.

Common Mistake

Students cancel (x + 2) and forget to check whether the restriction x ≠ −2 rules out their answer. They also sometimes rush the arithmetic when substituting back in to verify, missing a wrong answer.