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:
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(2x + 1) (x + 3) = 2x2 + x + 6x + 3 = 2x2 + 7x + 3
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(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
MC
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