Fractional Equations

Mikeybr

New member
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

Jameson

Staff member
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:

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

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 $(x-1)$.

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

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

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

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

$$\displaystyle x(x+1)+(x-1)(x+1)=3(x-1)$$

Can you solve from here?