Question

solve 1/x - 5/2x^2 = 8/5x

Answer 1

You really need to either use the equation editor or sufficient parentheses to make your meaning unambiguous. Is the middle term \[\frac{5}{2x^2}\]or is it\[\frac{5}{2}x^2\]Makes a big difference in the answer!

I'm going to assume this is what you meant:
\[\frac{1}{x}-\frac{5}{2x^2}=\frac{8}{5x}\]
My inclination would be to get rid of the fractions by multiplying through by all of the denominators:

\[x*2x^2*5x(\frac{1}{x}-\frac{5}{2x^2}) = x*2x^2*5x*\frac{8}{5x}\]\[10x^3-25x^2=16x^3\]Now factor out the common factors
\[x^2(10x-25) = x^2*16x\]Divide through by the common factor\[10x-25=16x\]I trust you can see how to solve it from here!

Answer 2

wait but there is no common factor :(

Answer 3

by the way you interpreted the question correctly, sorry for the confusion

Answer 4

the common factor was \(x^2\)

Answer 5

how?

Answer 6

I ended up with 10x^2-8 as my answer

Answer 7

but i don't think thats right

Answer 8

\[\color\red{ x^2}(10x-25) = \color\red{ x^2}(16x)\]

Answer 9

but where did the x^2 come from?

Answer 10

nevermind :) sorry

Answer 11

I factored it out:

\[10x^3-25x^2=16x^3\]\[x^2*10x-x^2*25=x^2*16x\]\[x^2(10x-25) = x^2(16x)\]

\[10x-25=16x\]Subtract \(10x\) from each side\[-25=6x\]\[x=-\frac{25}{6}\]

Answer 12

so did u get -4.12?

Answer 13

x = -4.12

Answer 14

yes ok or -25/6... ok, thanks :)

Answer 15

No, you should leave it as \[x=-\frac{25}{6}\]unless you've been specifically asked for a decimal number. And that decimal number would be -4.16666666666666666666666 etc.

Answer 16

why would you want an inconvenient, only approximate answer when you could have a compact, exact answer? :-)

Answer 17

I don't know :)

Answer 18

what about 2x-3/x + 4 = x - 3/x ? I got x^2 - 6x

Answer 19

I tried to do one of those equations so you could read it better but I was having trouble using it...

Answer 20

Okay, then put parentheses around each numerator or denominator or fraction

the original problem could have been written

(1/x) - (5/(2x^2)) = 8/(5x)

and there would be no question how to interpret it

Answer 21

(2x-3/x) + 4 = x - (3/x)

Answer 22

Better, but I still can't tell if the first term is

\[\frac{2x-3}{x}\] or\[2x-\frac{3}{x}\]