1. ## Help!

1. By eliminating the denominator, 5 + x/2x - 1 = x + 1/x

2. Solve for x: 3/2x +1 = x/2

3. 3x -7/2x - 3x-3/6x^2

2. ## Re: Help!

Hello,

Originally Posted by firecrack123
[COLOR=#000000][FONT=Helvetica Neue]1. By eliminating the denominator, 5 + x/2x - 1 = x + 1/x
I assume that you mean:
$\frac{5+x}{2x-1} = \frac{x+1}x~,~x\in \mathbb{R} \setminus \lbrace 0, \tfrac12 \rbrace$

If so: Multiply through by x*(2x-1). You'll get:

$(5+x) x = (x+1)(2x-1)~\implies~5x+x^2=2x^2+x-1 \\ x^2-4x-1=0$

Now use the formula to solve a quadratic equation.

2. Solve for x: 3/2x +1 = x/2
I assume that you mean:
$\frac3{2x+1} = \frac x2~,~x\in\matbb{R}\setminus \lbrace -\tfrac12 \rbrace$
If so: Multiply through by 2*(2x+1). You'll get:

$3 \cdot 2 = x \cdot (2x+1)~\implies~6=2x^2+x \\ 2x^2+x-6=0$

Now use the formula to solve a quadratic equation.

3. 3x -7/2x - 3x-3/6x^2
I leave the last one for you.