168k views
23 votes
Find all solutions to the problem: 2/x+6 - 1/x+3 =2


1 Answer

10 votes

Answer:


\displaystyle x=-(9)/(2),\:x=-4

Explanation:


\displaystyle (2)/(x+6)-(1)/(x+3)=2\\\\(2(x+3))/((x+6)(x+3))-((x+6))/((x+6)(x+3))=2\\ \\((2x+6)-(x+6))/((x+6)(x+3))=2\\ \\(x)/((x+6)(x+3))=2\\ \\x=2(x+6)(x+3)\\\\x=2(x^2+9x+18)\\\\x=2x^2+18x+36\\\\0=2x^2+17x+36


\displaystyle x=(-b\pm√(b^2-4ac))/(2a)\\\\x=(-17\pm√((17)^2-4(2)(36)))/(2(2))\\\\x=(-17\pm√(289-288))/(4)\\\\x=(-17\pm√(1))/(4)\\\\x=(-17\pm1)/(4)\\ \\x_1=(-18)/(4)=-(9)/(2),\: x_2=(-16)/(4)=-4

User Kasra Rahjerdi
by
7.2k points