Solve this linear equation...

[BigToque]

This was on a test I just wrote:

3/x-3 + 2/x-2 = 4/x^2-x-6

Here's a pic

 

[GodBlessTheUSA]

69

 

[Capn]

oops that's wrong, can't factor like that

 

[MrDingleDangle]

(3-sqrt(89))/5
(3+sqrt(89))/5

thanks mathmatica

 

[eakers]

factor the one on the right.
then multiply through and solve.

ta daaaaaaaaaaaaaaa.

*kat. <-- likes math.

 

[ArmenK]

3 and -18

 

[Antebios]

That's simple

x = SQRT(89) + 3
------------------
5

or x = -(SQRT(89) - 3)
-------------------
5

Yeah, baby, yeah. GENIUS!

 

[TheKidd]

I think the man needs a real explanation, not just an answer...

3/(x-3) + 2/(x-2) = 4/(x^(2)-x-6)
Factoring we get:
3/(x-3) + 2/(x-2) = 4/((x-3)(x+2))
Multiply by (x-3)(x+2)
3*(x+2) + (2(x-3)(x+2))/(x-2) = 4
Multiply by (x-2)
3*(x+2)(x-2) + 2(x^(2)-x-6) = 4x-8
Evaluate:
3x^(2) -12 + 2x^(2) - 2x -12 = 4x - 8
Simplify:
5x^(2) - 2x - 24 = 4x - 8
5x^(2) - 6x - 16 = 0

Quadratric Rule:
(-b +/- sqrt(b^(2) - 4ac))/2a
-(-6) +/- sqrt((-6)^(2) - (4*5*-16)))/(2*5)
(6 +/- sqrt (356))/10
(6 +/- 2*sqrt(89))/10
(3 +/- sqrt(89))/5

There you go.
BTW, Maple owns Mathematica.

 

[crypticlogin]

Mathematica is for thinkers, Maple is for engineering wannabes.

 

[TheKidd]

LOL, I am an engineering wannabe. I was just kidding by the way. I just think that maple is an efficient, simple to use program. I am sure that mathematica has some really nice math functions that maple can't even dream of doing. My Calc II textboook generates a lot of its diagrams with mathematica, so it must be a tight program.

 

[Triumph]

<< Mathematica is for thinkers, Maple is for engineering wannabes >>



and matlab rules them both.

 

[Triumph]

oh, and that equation isn't linear.

 

[Capn]

thekidd, you seem to be way too much of a fan of maple, wait a little while more I guess.

 

[Krakerjak]

17
9

 

[MeanMeosh]

5 / (x^2 - 5x + 6) = 4 / (x^2 - x - 6)

crossmultiply:

5(x^2 - x - 6) = 4(x^2 - 5x + 6)

5x^2 - 5x - 30 = 4x^2 - 20x + 24

x^2 + 15x - 54 = 0

x = ((-15 +/- sqrt(225 + 216)) / 2)

do not take my word on it though, check the algebra, mine's been rusty because of doing differential equations all semester...

 

[Shazam]

42