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))#