Question 242579
Solve the following rational expression:
{{{3/(x+2)+ 5/(x+4)=2}}}

I have been trying and have finished this question. I would just like to see if I have done it correstly. Thank you.


It would've helped greatly if you'd included your answer. This way, a check could've been made to see if your answer is correct. better yet, you could've done the check yourself, and would've determined if your answer is correct.


{{{3/(x+2)+ 5/(x+4)=2}}}


3(x + 4) + 5(x + 2) = 2(x + 2)(x + 4)----- Multiplying each side of the equation by its LCD, (x + 2)(x + 4) to clear the fractions


{{{3x + 12 + 5x + 10 = 2(x^2 + 6x + 8)}}}


{{{8x + 22 = 2x^2 + 12x + 16}}}


{{{0 = 2x^2 + 4x - 6}}} ------ Subtracting 8x and 22 from both sides of equation


{{{2x^2 + 4x - 6 = 0}}} ------ Rearranging equation 


{{{2(x^2 + 2x - 3) = 2(0)}}} ------ Factoring out GCF


(x + 3)(x - 1) = 0 ------ Factoring quadratic, {{{x^2 + 2x - 3 = 0}}} 


x  =  - 3, or  1


Since - 2 or - 4 would make the fractions in the equation undefined, then x CANNOT equal any of these 2 numbers. Since x DOES NOT equal - 2 or - 4, then x being equal to - 3 or 1 are the correct values. You can now do the check to make sure that they do work.