solve for x: (2/x)+(10/3x)=1
need help with this one, thanks
2006-11-19 07:41:42 · 4 answers · asked by BLUEEEE 1 in Science & Mathematics ➔ Mathematics
(2/x)+(10/3x)=1
find a common denominator
(6x + 10x)/(3x^2) = 1
cross-multiply and combine like terms
16x = 3x^2
3x^2 - 16x = 0
factor out an x
x(3x - 16) = 0
x = 0 3x - 16 = 0
3x = 16
x = 16/3
x cannot equal zero because a zero in the denominator means that the number is undefined, this is called an extraneous solution
ANSWER
x = 16/3
2006-11-19 08:02:32 · answer #1 · answered by trackstarr59 3 · 0⤊ 0⤋
The above is partially correct, but in a more complicated equation you are bound to lose answers if you go on multplying everything, the best way to solve this is to make all just one fraction:
(6x+10x)/(3x^2)=1
(16x - 3x^2)/(3x^2)=0 (-3x^2 is there because we transferred the 1 from the right side)
Now one x disappears and you have:
(16 - 3x)/(3x)=0
This is zero only in the case of the upperhand expression being equal to zero ansd therefore:
x=16/3
2006-11-19 07:57:12 · answer #2 · answered by Bax 2 · 0⤊ 0⤋
multiply both sides by x, so that
2 + 10/3 = x, then, by simplifying
x= (2*3 +10)/3 = 16/3
2006-11-19 07:45:10 · answer #3 · answered by kellenraid 6 · 0⤊ 1⤋
(6+10)/3=1x
16/3=x
2006-11-19 07:56:00 · answer #4 · answered by arash b 3 · 0⤊ 0⤋