Final answer:
The expression (x+1) / (x²+x-2)*(x²+5x+6)/ (3x+3) simplifies to (x+3) / 3(x-1) after factoring and cancelling out like terms from the numerator and denominator.
Step-by-step explanation:
To simplify the given expression, we first need to factorise the polynomials. The factors of the polynomials are as follows:
- x²+x-2 = (x-1)(x+2)
- x²+5x+6 = (x+2)(x+3)
- 3x+3 = 3(x+1) Substitute these factors back into the original expression. We get: (x+1) / (x-1)(x+2)*((x+2)(x+3))/ 3(x+1) As you can see, some terms appear both in the numerator and denominator, hence they can be cancelled out. After this step, we are left with: (x+3) / 3(x-1) This is the final simplified form of the initial expression.
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