Confused!

[School_girl]

:? Okey, well here is the problem that I need to slove 7/(x^2 - 5x) + 3/(5 - x) = 4/x ; I'll show you my work and maybe you can catch my mistake and help me out.

35-7x+3x^2-15x/5x^2-x^3-25x+5x^2=4/x

35-22x+3x^2/10x^2-x^3-25=4/x

Now, the confusion begins :idea: :!:


I took 4/x and tossed it over to the left side and made the equation equal to 0.

35-22x+3x^2/10x^2-x^3-25-4/x=0

40x^2+4x^3+100+35x-22x^2+3x/10x^3+x+25x=0

So I got:

7x^3+18x^2+35x+100=0

What do I do now??

 

[soroban]

Hello, School_girl!

Never ever leave those fractions in the equation . . .
. . Find the common denominator and multiply through.

7/(x^2 - 5x) + 3/(5 - x) = 4/x

I guess you didn't see that we can get a common denominator.

Factor the denominators:
. . . x² - 5x . = . x(x - 5)
. . . . . 5 - x . = . -(x - 5)

. . . . . . . . . . . . . . . . . . . . . . 7 . . . . . .3 . . . . . .4
The problem becomes: . ---------- - ------- . = . --
. . . . . . . . . . . . . . . . . . . .x(x - 5) . . x - 5 . . . . .x

. . . and clear denominators by multiply through by x(x - 5).

Can you finish it now?

 

[School_girl]

Yup, I got it. The answer is going to be 27/7.

Thanks!!!