Factorise and simplify the following equation: (2x^2 + 5x + 3) / (x + 1)

Firstly, you must factorise the quadratic equation on the numerator of the fraction. Observe that the x^2 has a coefficient of 2 and the term with no x terms is 3. 3 can only be factorised by 1 and 3. Also, notice that all signs are positive. Therefore we can set up two possibilities and by power of deduction, factorise the equation:

1. (2x + 1) (x + 3)         = 2x² + x + 6x + 3            = 2x² + 7x + 3       

2. (2x + 3) (x + 1)         = 2x² + 3x + 2x + 3          = 2x²+ 5x + 3

Number 2 is the correct expansion

So we have the following expression where we can cancel out the (x + 1) terms to get:

(2x + 3)(x + 1) / (x + 1)

= 2x + 3