# 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:

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

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:

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

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
$(u+3)$

So mulitiplying both sides by the above gives...

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

This gives a new equation without any fractions

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

solving for u gives

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

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

Solve the following equation for u:

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

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

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

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

$3 =-5(u+3)$

$3 =-5u-15$

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

$18 =-5u$

Divide both sides by -5

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

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?

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

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

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?

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

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

Did I do it right?
Not quite

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

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

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