Solve the following?

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1 Answer
seol
May 30, 2018

Note: The correct answer is here.

Explanation is wrong, I might come back and fix it later.

Explanation:

Common denominator shall be #(x+2)(x+5)#, so
#(2x(\color(red)(x+5)))/((x+2)(\color(red)(x+5)))=(3x(\color(blue)(x+2)))/((x+5)(\color(blue)(x+2)))-(1(\color(red)(x+5))(\color(blue)(x+2)))/((\color(red)(x+5))(\color(blue)(x+2))#

Now you have the same denominator overall. You can remove it to make your work easier.
#2x(x+5)=3x(x+2)-1(x+5)(x+2)#

Apply distributive property,
#2x(x)+2x(5)=3x(x)+3x(2)-\color(olive)((x+5)(x+2))#

We will do the green part later. First we simplify what I have distributed...
#2x^2+10x=3x^2+6x-\color(olive)((x+5)(x+2))#
#-x^2+4x=\color(olive)((x+5)(x+2))#

Now we will FOIL the green part.
#color(olive)((x+5)(x+2))=x(x)+x(2)+5(x)+5(2)#
#=x^2+2x+5x+10=x^2+7x+10#

And so...
#\therefore-x^2+4x=\color(olive)(x^2+7x+10)#

Moving everything to right side,
#0=2x^2+3x+10#

Now let's do quadratic formula, see here

Looks like we have an imaginary answer...
#-3/4\pmi\sqrt(71)/4#

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