Question

Find x ....
(2/x+2)+(1/x-2)=13/21

Answer 1

i tried solving but got x=37/13
to me it looks as if the problem should have 2 answers. i know that x=37/13 is wrong becuase i plugged it back in and it did not equal 13/21

Answer 2

\[\frac{ 2 }{ x+2 }+\frac{ 1 }{ x-2 } = \frac{ 13 }{ 21 }\] this?

Answer 3

Yes

Answer 4

Well first you have to get the two equations together by having them have the same denominator, so you multiply the left one by (x-2)/(x-2) and multiply the right one by (x+2)/(x+2) and you end up with (2x-4)/(x^2-4)+(x+2)/(x^2-4)=13/21, which simplifies to (3x-2)/(x^2+4)=13/21
Then you cross multiply to get 13(x^2-4)=21(3x-2), which then simplifies to
13x^2-52=63x-42 or 13x^2-63x+10=0 and then solve the quadratic

Answer 5

\[\frac{ (x-2)(2)+(1)(x+2) }{ (x+2)(x-2) } = \frac{ 13 }{ 21 }\]

Answer 6

\[\frac{ 2x-4+x+2 }{ (x+2)(x-2) } = \frac{ 13 }{ 21 }\]

Answer 7

\[\frac{ 3x-2 }{ (x+2)(x-2) } = \frac{ 13 }{ 21 } \implies (3x-2)(21) = (13)(x+2)(x-2)\]

Answer 8

\[63x-42=13x^2-52 \implies 13x^2-63x-20=0\] I'll let you finish it off