4. Simplify the following rational expression:𝑥2+2𝑥−15𝑥2+11𝑥+30=
Question
- Simplify the following rational expression:𝑥2+2𝑥−15𝑥2+11𝑥+30=
Solution
Sure, let's simplify the given rational expression step by step.
The given expression is (x^2 + 2x - 15) / (x^2 + 11x + 30).
Step 1: Factorize the numerator and the denominator.
The numerator x^2 + 2x - 15 can be factorized into (x - 3)(x + 5).
The denominator x^2 + 11x + 30 can be factorized into (x + 5)(x + 6).
So, the expression becomes (x - 3)(x + 5) / (x + 5)(x + 6).
Step 2: Cancel out the common factors.
Here, (x + 5) is a common factor in the numerator and the denominator. So, we can cancel it out.
After cancelling out, we get the simplified expression as (x - 3) / (x + 6).
So, the simplified form of the given rational expression is (x - 3) / (x + 6).
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