How do you solve this equation?

Question

(x/64) - (1/x) / 1 + (8/x)

Can someone please explain

Answer 1

(x/64) - (1/x) = x(x/64) - 64(1/x) = { (x^2) -64} / 64x

the denominator is 1 +(8/x) = (x/x) + (8/x) = (8+x)/x

so { (x^2) -64}/64x divided by (8+x)/x is
{ (x^2) -64} /64x multiplied by x/ (8+x)
= { (x+8)(x-8) } /64x * x/ (8+x)

= { (8+x)(8-x)x } / { 64x (8+x) }
= (8-x) /64

Answer 2

Since the (1/x)/1 is kind of silly (dividing by 1 doesn't do much)

AND you need an = to make in an equation, not an expression,

maybe you mean (x/64)-1/x = 1+(8/x)

That would mean (x/64)-1=1/x + 8/x
x/64-1=9/x
(x^2)/64-x=9
(x^2)/64-x-9=0

Then you can use the quadratic formula
x=sqrt(b^2+/- 4ac)/2a

Answer 3

the problem is incomplete unless there is equality or inequality sign.

Anyway, i assume that it is: (x/64)-(1/x)/ 1+(8/x)=0

numerator: (x/64)-(1/x)
denominator: 1+(8/x)

lets simplify the numerator first;

the lcd here is 64x

if we multiply the LCD to the 2 terms we got (x^2-64)

now, the lcd in the denominators is (x)

if we multiply the LCD to the 2 terms we got (x+8)

now we have a less complex term: (x^2-64)/(x+8)=0

the numerator can be simplified to (x-8)(x+8)

so, (x-8)(x+8)/(x+8)=0 is x-8=0

thus; x=8

checking:

(8/64)-(1/8)/ 1+(8/8)=0
(1/8)-(1/8)/1+1=0
0/2=0
0=0 TRUE

Answer 4

It does need an equal sign. Let's assume that it's equal to c

{(x/64)-(1/x)}/{1+(8/x)} = c Multiply by 1+8/x
x/64 - 1/x = c + 8c/x Multiply by x
x^2/64 - 1 = cx + 8c This is a quadratic. Get all of it to one side.
x^2/64 - cx - (8c+1) = 0 Solve for x.

x = 32{c +- sqrt(c^2 + (8c+1)/16)} and x is not 0.

Answer 5

That's not an equation, it's an expression.

Simplified, the expression is

(x / 64) + (7 / x) or (x^2 + 448) / 64x

Answer 6

I'll assume that it is
(x/64) - (1/x) / (1 + (8/x))=1
solving...
x.x -64/(64x) * 8/(x+8)=1
(x-8)=1
x=8

which is incorrect as if we put 8 back into the equaltion we get 0/2 which is equal to ∞

Either the question is wrong or you have put it incorrectly.

Answer 7

do you know what an equation is??? it needs an = sign which is missing from your question. It is not an equation to be solved but a bunch of numbers and a variable put together.

Answer 8

if by this you mean
((x/64) - (1/x))/(1 + (8/x))
((x^2 - 64)/(64x)) / ((x + 8)/x)
((x^2 - 64)/(64x)) * (x/(x + 8))
(x(x^2 - 64))/(64x(x + 8))
(x(x + 8)(x - 8))/(x(x + 8) * 64)

ANS : (x - 8)/(64)

Answer 9

An equation should have a = sign otherwise it is not an equation.

If / is reffered as = the the answer can be found

Answer 10

It's not an equation. There is no = sign.