help w/ math homework...factoring..please!!!?

[Ruthie S]

(x/6) + (15/x) = (5/6)
Find x.

Please tell me how to approach this program...step by step..
I have an exam tomorrow and I need help in factoring.
thanks. Much appreciated
thanks a bunch!!!!!!!!!!

[ahmed g]

=(x^2+90)/6x=5/6
x^2+90=5
x=i(85)^.5

[mathland]

Our LCD is 6x.

So, multiply 6x by every term on both sides of the fractional equation to remove the fractions.

x/6 times 6x = x^2

15/x times 6x = 90

5/6 times 6x = 5x

We now have:

x^2 + 90 = 5x

Subtracting 5x from both sides of the equation, we get this:

x^2 - 5x + 90 = 0

The above cannot equation cannot be factored.

So, we use the quadratic formula where a = 1, b = -5 and
c = 90.

x = -(-5) +- sqrt{(-5)^2 - 4(1)(90)}/2(1)

x = 5 + - sqrt{25 - 360}/2

x = 5 +- sqrt{-335}/2

Your solution will be two complex numbers involving the letter i.

In math, we cannot take the square root of a negative number.

So, we multiply sqrt{-335} by sqrt{-1}.


The sqrt{-1} = i

We now have:

x = 5 +- sqrt{335}i/2

Our two solutions:

x = 5 + sqrt{335} i

AND

x = 5 - sqrt{335} i

Done!

Note: Sometimes, your answer will not be a real number.

Also, factoring means to UNDO MULTIPLICATION by finding factors.