Homework Help: Finding x with fractions

Or, possibly:[tex]\frac{1}{3x-7}-\frac{2}{5x-5}-\frac{3}{3x+1}=0[/tex]... have you tried #1 and #2 at all?

#3 was:[tex] (x+7)^{1/2} - (x+2)^{1/2} = (x-1)^{1/2}-(x-2)^{1/2}[/tex]... notice that x ≥ 2 for the RHS to be real?

 

It becomes easier if you rearrange the equation before squaring:

[tex](x+7)^{1/2} - (x-1)^{1/2}= (x+2)^{1/2} -(x-2)^{1/2}[/tex]

ehild

 

Taking the square of both sides and expand

[tex](x+7) + (x-1)-2\sqrt{(x+7)(x-1)}= (x+2) +(x-2)-2\sqrt{(x-2)(x+2)}[/tex]
the x terms cancel, simplify and divide by 2:
[tex]3-\sqrt{(x+7)(x-1)}= -\sqrt{x^2-4}[/tex]
or [tex]3+\sqrt{x^2-4}= \sqrt{x^2+6x-7}[/tex]
Square again. The x² terms cancel and you get a simple equation for x.

ehild

 

An additional comment:

Once you do that last step, you will still have a square root. Fortunately at that point, the equation you are left with is fairly simple (uncomplicated).