MHB Fractional Equation Help: Solve 3 Problems

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The discussion centers around three fractional equation problems that the user is struggling to solve. The first equation can be simplified by eliminating fractions through multiplication by the denominators. A suggestion is made to rewrite the first fraction and then multiply through by the denominators to simplify the equation further. The importance of careful notation, especially with parentheses, is emphasized to facilitate better assistance. The thread encourages users to tackle one problem at a time for more effective help.
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There are three problems on my homework I can't get quite right.

x/x-1 - 1 = 3/x+1

4/b - 1/b+3 = 3b+2/b^2+2b-3

3r+1/r+3 + 2 =5r-2/r+3
 
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Mikeybr said:
There are three problems on my homework I can't get quite right.

x/x-1 - 1 = 3/x+1

4/b - 1/b+3 = 3b+2/b^2+2b-3

3r+1/r+3 + 2 =5r-2/r+3

Hi Mikeybr. Welcome to MHB! :)

Try posting one question at a time please and show some attempt at it. This helps us help you more efficiently. Also, be careful with parentheses!

I believe #1 is the following:

[math]\frac{x}{x-1}-1=\frac{3}{x+1}[/math]

You could do this a few ways but the idea is to get rid of the fractions somehow. Let's first try to rewrite the first fraction by multiplying everything by $(x-1)$.

[math](x-1) \cdot \frac{x}{x-1} -1 \cdot (x-1) = (x-1) \cdot \frac{3}{x+1}[/math]

The first fraction now has [math]\frac{x-1}{x-1}[/math] in it, which is 1 so that fraction is now just x. The rest of the equation is below.

[math]x - (x-1) = \frac{3(x-1)}{x+1}[/math]

Now we want to change the other fraction, so we can multiply everything by $(x+1)$. Doing that we get:

[math]x(x+1)+(x-1)(x+1)=3(x-1)[/math]

Can you solve from here?
 
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