# Thread: Simplifying Fractions and solving for u

1. ## Simplifying Fractions and solving for u

Could someone explain how to do this problem?

Solve the following equation for u:

$\displaystyle \frac{3}{u+3} =-5$

I couldn't find how to do this in my notes.

2. Originally Posted by eraser851
Could someone explain how to do this problem?

Solve the following equation for u:

$\displaystyle \frac{3}{u+3} =-5$

I couldn't find how to do this in my notes.

You want to clear the fractions by multiplying by the LCD in this case
$\displaystyle (u+3)$

So mulitiplying both sides by the above gives...

$\displaystyle (u+3) \cdot \frac{3}{u+3} =-5 \cdot (u+3)$

This gives a new equation without any fractions

$\displaystyle 3=-5(u+3) \iff 3=-5u-15$

solving for u gives

$\displaystyle u=\frac{-18}{5}$

3. Originally Posted by eraser851
Could someone explain how to do this problem?

Solve the following equation for u:

$\displaystyle \frac{3}{u+3} =-5$

I couldn't find how to do this in my notes.
$\displaystyle \frac{3}{u+3} =-5$

Multiply both sides by $\displaystyle u+3$, the LCD

$\displaystyle \frac{3(u+3)}{u+3} =-5(u+3)$

$\displaystyle 3 =-5(u+3)$

$\displaystyle 3 =-5u-15$

$\displaystyle 3+15 =-5u-15+15$

$\displaystyle 18 =-5u$

Divide both sides by -5

$\displaystyle u =\frac{-18}{5}$

4. Okay, I think I've got it now.

I got a new problem with the same format. Could someone please check my answer to make sure I did it right?

$\displaystyle \frac{3}{x-1}=-2$

Multiplied both sides by (x-1)
$\displaystyle 3=-2x-2$
$\displaystyle 5=-2x$
And then divide both sides by -2.
$\displaystyle x=\frac{-5}{2}$

Did I do it right?

5. Originally Posted by eraser851
Okay, I think I've got it now.

I got a new problem with the same format. Could someone please check my answer to make sure I did it right?

$\displaystyle \frac{3}{x-1}=-2$

Multiplied both sides by (x-1)
$\displaystyle 3=-2x-2$
$\displaystyle 5=-2x$
And then divide both sides by -2.
$\displaystyle x=\frac{-5}{2}$

Did I do it right?
Not quite

$\displaystyle (x-1) \cdot \frac{3}{x-1}=-2(x-1)$

When the -2 is multiplied in you should get...

$\displaystyle 3= -2x+2 \iff x=-\frac{1}{2}$