Question

I need help solving 1/x+1/x+4=1/4

Answer 1

Welcome to Openstudy!

Answer 2

\[\Large \frac{ 1 }{ x }+\frac{ 1 }{ x+4 }=\frac{ 1 }{ 4 }\]

Is this your question?

Answer 3

yes

Answer 4

the lcd is 4x, right? but after that I am lost

Answer 5

Ok

Answer 6

No it's not. With a question like this, it is very tedious yes, but the lcd (when you have two unlike denominators with variables) is the product of the two

Answer 7

so lcd=x(x+4)

Answer 8

\[\Large [x(x+4)] \times\frac{ 1 }{ x }+\frac{ 1 }{ x+4 }=\frac{ 1 }{ 4 } \times [x(x+4)]\]

Answer 9

You could add a 4 in there to avoid one step, doesn't really matter

Answer 10

\[\Large (x+4)+(x)=\frac{[x(x+4)]}{4}\]

Answer 11

multiplying both sides by 4

Answer 12

\[\Large 4[(x+4)+x]=x(x+4)\]

Answer 13

ok I factored to get: 8x+16= x^2 +4x

Answer 14

That's correct

Answer 15

Go on from there

Answer 16

x^2-4x-16=0 is what you end up with

Answer 17

will i make this equation equal zero?

Answer 18

Yes

Answer 19

you gotta use the quadratic equation:
http://www.math.com/students/calculators/source/quadratic.htm

Answer 20

where a=1 b=-4 and c=-16

Answer 21

i figured that bc I couldn't factor it out. okay

Answer 22

[2-\sqrt{20}, 2+\sqrt{20}\]