(a+2)/(a²+a-2) + 3/(a²-1) | Simplification of Rational Expressions | SciPiPupil

Question: Simplify: $\dfrac{a+2}{a² +a -2} +$$\dfrac{3}{a² -1}$

Solution:

Given,

$= \dfrac{a+2}{a² +a -2} +\dfrac{3}{a² -1}$

$= \dfrac{a+2}{a² +(2-1)a -2} +\dfrac{3}{a² -1}$

$= \dfrac{a +2}{a² +2a -a -2} +\dfrac{3}{a² -1}$

$= \dfrac{a +2}{a(a +2) -1(a+2)} +\dfrac{3}{a² -1}$

$= \dfrac{a+2}{(a-1)(a+2)} +\dfrac{3}{a² -1}$

$= \dfrac{1}{a -1} +\dfrac{3}{(a+1)(a-1)}$

$= \dfrac{1(a+1) +3}{(a-1)(a+1)}$

$= \dfrac{a +1 +3}{a²-1}$

$= \dfrac{a +4}{a² -1}$

= Answer

Related Notes and Solutions:

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