I know that you have to find the LCD, but I am unsure where to go from there?! Any help would be great.
12 / 3x - 2 + 5 / x + 4 = 1
2007-04-05 07:57:52 · 3 answers · asked by jdawg21s 1 in Science & Mathematics ➔ Mathematics
If you multiply everything by the LCD, you'll get rid of the fractions.
I assume the equation is this:
12/(3x - 2) + 5/(x + 4) = 1
(PLEASE use parentheses in the future!!)
If you multiply all terms by (3x-2)(x+4), you'll get:
12(x+4) + 5(3x-2) = (3x-2)(x+4)
12x + 48 + 15x - 10 = 3x^2 + 10x - 8
27x + 38 = 3x^2 + 10x - 8
0 = 3x^2 - 17x - 46
0 = (3x - 23)(x + 2)
x = 23/3 or -2
2007-04-05 08:04:13 · answer #1 · answered by Mathematica 7 · 0⤊ 0⤋
The common denominator is 3x. Multiply every term by 3x to elimate the denominators. Then solve the equation.
12/3x - 2 + 5/x + 4 = 1
12 - 6x + 15 + 12x = 3x Move all x terms to left and numbers to right.
3x = -27
x = -9
Check:
12/(-27) -2 + 5/(-9) + 4 = 1 Simplify anything possible.
-4/9 - 2 - 5/9 + 4 = 1 Combine fractions. -9/9 = -1
-1 -2 + 4 = 1
-3 + 4 = 1 Correct.
2007-04-05 15:05:11 · answer #2 · answered by ecolink 7 · 0⤊ 0⤋
Actually, just multiply by the LCD. And in case of extraneous solutions, remember the none of the original denominators can equal zero.
2007-04-05 15:03:35 · answer #3 · answered by Anonymous · 0⤊ 0⤋