It is probably very easy and straightforward question. But I like to see how many ways you can do it. Please do one step at a time in separate lines and text not too "crowded" Thanks
1 / x-4 + 2 / x^2 -16 = 3 / x + 4
2007-04-18 18:50:39 · 6 answers · asked by mysteriousjz 2 in Science & Mathematics ➔ Mathematics
To solve equations with fractions, you need to multiply each term by the LCD/1. The LCD in this case is (x + 4)(x - 4) which is also the factorization of the center term.
When you multiply each term by the LCD/1, the denominators will "cancel out."
So this becomes:
[(x + 4)(x - 4)/1 * 1/(x - 4)] + [(x + 4)(x - 4)/1 * 2/(x + 4)(x - 4)] = [(x + 4)(x - 4)/1 * 3/(x + 4)]
Now you can cancel out the denominators to get:
1*(x + 4) + 2 = 3(x - 4)
Expand to get: x + 4 + 2 = 3x - 12
Collect like terms and solve for x:
x + 6 = 3x - 12
18 = 2x
x = 9
Now you would eliminate any values that result in a denominator of zero, i.e. x = 4 or -4, but in this case that is not the case, and your solution is x = 9.
good luck!
2007-04-18 18:53:38 · answer #1 · answered by birdwoman1 4 · 0⤊ 0⤋
since this is an equation you can multiply each term by the LCD which is (x-4)(x+4). That comes from factoring x^2-16 and looking at the other denominators.
(x-4)(x+4)(1/(x-4)) +(x-4)(x+4)(2/(x-4)(X+4)) = (x-4)(x+4)(3/(x+4))
Now Cancel:
In the first term the (x-4)'s cancel
In the second term the (x-4)(x+4)'s cancel
and on the right side of the equation the (x+4)'s cancel.
This leaves
(x+4) + 2 = 3(x-4)
Simplify
x+4 +2 = 3x-12
x+6 = 3x-12
2x = 18
x = 9
Because of having variables in the denominator you must make sure that this solution is not excluded. Your exclusions are 4 and neg 4 so the solution is 9.
2007-04-19 02:03:34 · answer #2 · answered by lizzie 3 · 0⤊ 0⤋
x=1
2007-04-19 01:54:42 · answer #3 · answered by dianneiyisan 3 · 0⤊ 0⤋
Without going thru all the gory details, the denominator of the second term is (x-4)(x+4).
This suggests that you make this the denominator for all terms. I'm sure that after all the multiplications, collection of terms and the like, the answer will pop up.
2007-04-19 01:56:56 · answer #4 · answered by cattbarf 7 · 0⤊ 0⤋
1 / (x-4) + 2 / (x^2 -16) = 3 / (x + 4)
1 / (x-4) + 2 / (x+4)(x-4) = 3 / (x + 4)
x+4 +2 = 3(x-4)
x+6 =3x-12
18=2x
9=x
2007-04-19 02:03:12 · answer #5 · answered by ironduke8159 7 · 0⤊ 0⤋
multiply everything by xsqrd -16 so u get (x+4)+2=3(x-4)
x+6=3x-12 is 0=2x-18 so x=9
2007-04-19 01:57:25 · answer #6 · answered by dpmwcml 2 · 0⤊ 0⤋