Find the exact solution(s) to this equation
(3)/(3x+4) + (2)/(x-1) = 2
and show your work
2006-10-24 19:30:23 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
why am i getting people with different answers???!!! cmon people i said experienced math people only who know what they're doing!!!
2006-10-24 19:55:12 · update #1
(3/(3x+4))+(2/(x-1))=2
3(x-1)+2(3x+4)
------------------- = 2
(3x+4)(x-1)
3x-3+6x+8
------------------- = 2
3x^2 +4x -3x -4
9x+5
------------- = 2
3x^2 +x -4
9x+5 = 6x^2 +2x -8
0=6X^2 -7x -13
0=(6x-13)(x+1)
x=-1 or x=13/6
Those are the two answers.
----
Unfortunately the first poster multiplied wrong at one step.
Substitute these answers in to check them out.
2006-10-24 19:47:19 · answer #1 · answered by DadOnline 6 · 2⤊ 1⤋
3 / (3x + 4) + 2 / (x - 1) = 2
Multiply both sides by (3x + 4)(x - 1).
3(x - 1) + 2(3x + 4) = 2(3x + 4)(x - 1)
Expand both sides.
3x - 3 + 6x + 8 = 6x^2 + 2x - 8
Gather like powers to one side.
6x^2 - 7x - 13 = 0
Factorise.
(6x - 13)(x + 1) = 0
Thus, either 6x - 13 = 0, which gives x = 13 / 6,
or, x + 1 = 0, which gives x = -1.
2006-10-24 22:16:19 · answer #2 · answered by falzoon 7 · 1⤊ 0⤋
(3)/(3x+4) + (2)/(x-1)= 2
[3(x-1)+2(3x+4)] / [(3x+4)(x-1)] =2
3(x-1) + 2(3x+4) = 2 (3x+4)(x-1)
3x-3 + 6x+8 = (6x+8) (x-1)
9x+5=6x^2 +2x-8
6x^2-7x-13=0
(6x-13)(x+1)=0
x= 13/6 or x= -1
2006-10-24 22:47:45 · answer #3 · answered by Anonymous · 0⤊ 0⤋
(3)/(3x+4)+ (2)/ (x-1)
you need a common denominator, so multiply both sides by the other sides' denominator
{[(x-1)/(x-1)][(3)/(3x+4)]}+ {[(3x+4)/(3x+4)][(2)/(x-1)]}= 2
which simplifies to:
[(3x-3)+(6x+8)]/ (3x^2+x-4)= 2
which simplifies to:
(9x-5)/(3x^2+x-4)=2
Then divide 2 by the base of the fraction (which is actually the same as multplying it)
(9x-5)= 2 [3x^2+x-4]
multiply through...
9x-5= 6x^2+2x-4
bring it all over to one side
0=6x^2-7x+1
0= (6x-1)(x-1)
So x= 1, and 1/6
2006-10-24 19:32:34 · answer #4 · answered by legallyblond2day 5 · 1⤊ 1⤋
i made a mistake. the solution is : x={ 7+(312*1/2) } /12 or
x={ 7-(312*1/2) } /12
(couldn't find the symbol of sqr so i wrote it as : *1/2 )
2006-10-25 09:09:32 · answer #5 · answered by trankssj 1 · 0⤊ 0⤋
William B and falzoon are both correct and both naturally have the same answers. It
only cost you two points.
2006-10-24 22:47:21 · answer #6 · answered by sydney m 2 · 0⤊ 0⤋
Just so you know, William B has the right answer, without doubt.
2006-10-24 20:02:21 · answer #7 · answered by Jimbo 5 · 1⤊ 0⤋
he he he both have almost the right answer
2006-10-24 20:47:44 · answer #8 · answered by gjmb1960 7 · 0⤊ 0⤋