1. ## Qudratic equations???

√x/(x – 1) + √(x – 1)/x = 2(1/6)

Please find solution for x(with steps), I find it very difficult especially with the unnecessary roots I find even after squaring!!!!

the answer is : x = - 4/5, 9/5

2. Hi
Originally Posted by ice_syncer
√x/(x – 1) + √(x – 1)/x = 2(1/6)

Please find solution for x, I find it very difficult especially with the unnecessary roots I find even after squaring!!!!
Is it $\frac{\sqrt{x}}{x-1}+\frac{\sqrt{x-1}}{x}=\frac{2}{6}$ (that's what you wrote) or $\sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{2}{6}$ ?

3. Originally Posted by flyingsquirrel
Hi

Is it $\frac{\sqrt{x}}{x-1}+\frac{\sqrt{x-1}}{x}=\frac{2}{6}$ (that's what you wrote) or $\sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{2}{6}$ ?

well, actually that's exactly what the assignment says

√x/(x – 1) + √(x – 1)/x = 2(1/6)

:
x = - 4/5, 9/5

4. Originally Posted by ice_syncer
√x/(x – 1) + √(x – 1)/x = 2(1/6)

Please find solution for x(with steps), I find it very difficult especially with the unnecessary roots I find even after squaring!!!!

the answer is : x = - 4/5, 9/5
The correct equation is $\sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{13}{6}$.

Square both sides:

$\frac{x}{x-1} + 2 + \frac{x-1}{x} =\frac{169}{36}$.

Multiply both sides by $36 (x - 1) x$:

$36 x^2 + 72 x (x - 1) + 36 (x - 1)^2 = 169 x (x - 1)$

Expand and simplify into a routine quadratic equation. Solve the quadratic equation. Substitute the solutions into the original equation and reject the ones (if any) that fail to satisfy it.

5. Originally Posted by mr fantastic
The correct equation is $\sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{13}{6}$.

Square both sides:

$\frac{x}{x-1} + 2 + \frac{x-1}{x} =\frac{169}{36}$.

Multiply both sides by $36 (x - 1) x$:

$36 x^2 + 72 x (x - 1) + 36 (x - 1)^2 = 169 x (x - 1)$

Expand and simplify into a routine quadratic equation. Solve the quadratic equation. Substitute the solutions into the original equation and reject the ones (if any) that fail to satisfy it.
ok

6. Originally Posted by mr fantastic
The correct equation is $\sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{13}{6}$.

Square both sides:

$\frac{x}{x-1} + 2 + \frac{x-1}{x} =\frac{169}{36}$

Subtract 2 from both sides:

${\color{red}\Rightarrow \frac{x}{x-1} + \frac{x-1}{x} =\frac{97}{36}}$

Multiply both sides by $36 (x - 1) x$:

[snip]
You can make life a little easier by first doing what I added (in red).

7. Originally Posted by mr fantastic
You can make life a little easier by first doing what I added (in red).
yeah I did that before your requoting, thanks anyway