Question

HELP ME QUICK PLEASEEEE solve for x: 2/x-2+7/x^2-4=5/x

Answer 1

`\displaystyle\\\\(2)/(x-2)+(7)/(x^2-4)=(5)/(x)\\\\(^(x+2))2~~~~~)/(x-2)+(7)/((x-2)(x+2))=(5)/(x)\\\\(2(x+2))/((x-2)(x+2))+(7)/((x-2)(x+2))=(5)/(x)\\\\(2x+4+7)/(x^2-4)=(5)/(x)\\\\(2x+11)/(x^2-4)=(5)/(x)\\\\5(x^2-4)=x(2x+11)\\\\5x^2-20=2x^2+11x\\\\5x^2-2x^2 -11x-20=0`

`\displaystyle\\3x^2-11x-20=0\\\\x_(1,2)=(-b\pm√(b^2-4ac))/(2a)=(11\pm√(121+4\cdot3\cdot20))/(2\cdot3)=\\\\=(11\pm√(121+240))/(6)=(11\pm√(361 ))/(6)=(11\pm19)/(6)\\\\x_1=(11-19)/(6)=(-8)/(6)\\\\\boxed{\bf x_1=-(4)/(3)}\\\\x_2=(11+19)/(6)=(30)/(6)\\\\\boxed{\bf x_2=5}`