How do you simplify $(2x + 3)/( x + 3) + x/ (x - 2)$ ?

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Answer 1 · 2017-10-28T21:37:52

It is a little strange:

$(1/3)((3x+(1+sqrt(19)))(3x+(1-sqrt(19))))/((x+3)(x-2))$

$(2x+3)/(x+3)+x/(x-2)$

$=(x-2)/(x-2)(2x+3)/(x+3)+(x+3)/(x+3)x/(x-2)$

$=(2x^2+3x-4x-6+x^2+3x)/((x+3)(x-2))$

$=(3x^2+2x-6)/((x+3)(x-2))$

Now we must find the roots of:

the denominator:

$x=(-2+-sqrt(2^2-4*3*(-6)))/(2*3)$

$x=(-2+-sqrt(76))/(6)$

$x=(-1+-sqrt(19))/(3)$

So the polynomium simplifies to:

$3((x+(1+sqrt(19))/(3))(x+(1-sqrt(19))/(3)))/((x+3)(x-2))$

$(1/3)((3x+(1+sqrt(19)))(3x+(1-sqrt(19))))/((x+3)(x-2))$

How do you simplify (2x + 3)/( x + 3) + x/ (x - 2)(2x + 3)/( x + 3) + x/ (x - 2)?