Question

Find all solutions to the problem: 2/x+6 - 1/x+3 =2
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Answer 1

`\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`