SOLUTION: 5/x + 7/6 = 4/(x-4), solve for x. I am confused as to how I come up with the LCD for these to be able to solve for x

Algebra ->  Expressions-with-variables -> SOLUTION: 5/x + 7/6 = 4/(x-4), solve for x. I am confused as to how I come up with the LCD for these to be able to solve for x      Log On


   

Question 172130: 5/x + 7/6 = 4/(x-4), solve for x.
I am confused as to how I come up with the LCD for these to be able to solve for x
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
5%2Fx+%2B+7%2F6+=+4%2F%28x-4%29
If you multiply each side by 6x%2A%28x+-+4%29,
that will guarantee that no fractions will
be left
5%2A6%2A%28x+-+4%29+%2B+7x%2A%28x+-+4%29+=+4%2A6%2Ax
30%2A%28x+-+4%29+%2B+7x%2A%28x+-+4%29+=+24x
30x+-+120+%2B+7x%5E2+-+28x+=+24x
7x%5E2+-+22x+-+120+=+0
Use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+7
b+=+-22
c+=+-120
x+=+%28-%28-22%29+%2B-+sqrt%28+%28-22%29%5E2-4%2A7%2A%28-120%29+%29%29%2F%282%2A7%29+
x+=+%2822+%2B-+sqrt%28+484+%2B+3360+%29%29+%2F+14+
x+=+%2822+%2B-+sqrt%283844%29%29+%2F+14+
x+=+%2822+%2B+62%29+%2F+14+
x+=+6
and
x+=+%2822+-+62%29+%2F+14
x+=+-%2820%2F7%29
I checked both answers, and they look right

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Your 3 denominators are x, 6, and (x-4). Not a common factor among them. You are stuck with using the product of the three, namely x%286%29%28x-4%29=6x%5E2-24x

The good news is, once you apply the LCD to all three fractions, you can simply eliminate the denominators by multiplying both sides of the equation by the LCD. You only have to deal with the numerators.