How can I solve this?
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Question

How can I solve this?
http://newton.matem.unam.mx:8080/ejercicios/racionales/p0716.gif

***[isuru]*** · Answer

hi,
 do u want to solve it for "s" ?

osanseviero · Answer

Yep

***[isuru]*** · Answer

soo...
   $$\frac{ 4s -2  }{ 9 } - \frac{ 3s-6 }{ 5s -4 } =\frac{ 2s -1 }{6 }$$

write left hand side taking a common denominator...
$$\frac{ (4s -2)(5s -4) -9(3s -6) }{ 9(5s -4) }$$

now cross multiply it....
$$\frac{ (4s -2)(5s -4) - 9(3s -6) }{ 9(5s -4)  } = \frac{ (2s -1) }{6 }$$$$6(4s -2)(5s -4) - 54(3s -6) =9 (2s -1)(5s -4)$$

Now let's start simplifying it...

divide the whole system by 3..
$$2(4s -2)(5s -4) - 18(3s -6) =3 (2s -1)(5s -4)$$

$$2[20s ^{2} - 26s +8] - 54s + 108 = 3[10s ^{2} -13s +4 ]$$
$$40s ^{2} - 52s +16 - 54s + 108 = 30s ^{2} -39s +12  $$$$10s ^{2} -67s  +112 = 0$$$$s = 3.5 \ and \ s =3.2$$

hope this will help ya!!

P.S - I didn't use a cal.. so there may be flaws ... But I am perfectly sure about the method...Soo try it for urself  XD

osanseviero · Answer

I think it is right, thanks a lot