SOLUTION: I'm homeschooled, and I've been working on this problem for a long time. My mother gave me the answer, but I can't seem to work the steps out. The question is: What are the sol

Question 422034: I'm homeschooled, and I've been working on this problem for a long time. My mother gave me the answer, but I can't seem to work the steps out.
The question is:
What are the solutions to the equation 1 + (1/x^2) = (3/x).
The answer is:
x = (3/2) + ((sqrt 5)/2); x = (3/2) - ((sqrt5)/2)
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Multiply EVERY term by the LCD to clear out the fractions.

Subtract 3x from both sides.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

or Break up the expression.

So the solutions are or

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What are the solutions to the equation 1 + (1/x^2) = (3/x).
Multiply thru by x^2 to get rid of the denominators:
x^2 + 1 = 3x
---
Rearrange:
x^2-3x+1 = 0
-----
Use the quadratic formula to get:
x = [3 +- sqrt(9-4*1)]/2
---
x = [3 +- sqrt(5)]/2
===
x = (3/2)+(1/2)sqrt(5) or x = (3/2)-(1/2)sqrt(5)
===================================================
Cheers,
Stan H.
============
RELATED QUESTIONS
x^2 + 2x + 2 = 0 I am homeschooled, and I've been working a long time on this... (answered by jim_thompson5910)
I am homeschooled and I have worked on this problem for hours. My mom finally gave me... (answered by mananth)
I am homeschooled and I have worked on this problem for hours. My mom finally gave me... (answered by sudhanshu_kmr)
Hi, i've been working on this some for days and cant seem to solve it, I would ask my... (answered by MathLover1)
I am homeschooled and I have worked on this problem for hours. My mom finally gave me... (answered by mananth)
I am homeschooled and I have worked on this problem for hours. My mom finally gave me... (answered by robertb)
I am homeschooled and I have worked on this problem for hours. My mom finally gave me... (answered by edjones)
Hi! I've been trying this problem for some time and I can't seem to figure it out. A... (answered by ikleyn,MathTherapy)
I am homeschooled and I have worked on this problem for hours. My mom finally gave me... (answered by ankor@dixie-net.com)