Simplify the following rational expression:𝑥2+10𝑥+25𝑥2+7𝑥+10

Sure, let's simplify the given rational expression step by step.

The given expression is (x^2 + 10x + 25) / (x^2 + 7x + 10).

Step 1: Factorize the numerator and the denominator.

The numerator x^2 + 10x + 25 can be factorized to (x + 5)^2. The denominator x^2 + 7x + 10 can be factorized to (x + 2)(x + 5).

So, the expression becomes (x + 5)^2 / (x + 2)(x + 5).

Step 2: Cancel out the common factors.

The common factor (x + 5) in the numerator and the denominator can be cancelled out.

So, the simplified form of the given rational expression is (x + 5) / (x + 2).