Operation (arrow) defined by a(arrow)b = a + b / a - b

[Love21]

Let the operation (arrow) be defined by a (arrow) b = a + b / a - b for all numbers a and b, where a is not equal to b.

If 1 (arrow) 2 = 2 (arrow) x, what is the value of x?

(a) 4
(b) 3
(c) 2
(d) 1
(e) 0

So i did 1 + 2 / 1 -2 = 3/-1 = -3
Now i'm not sure how to proceed with the 2 (arrow) x part
Can someone help me?

 

[Loren]

Re: Operation with arrows

You say ... a (arrow) b = a + b / a - b.

a + b / a - b means $\displaystyle a+\frac{b}{a}-b$. Is that what you mean? If not, you should use parenthesis to better indicate what is meant. For instance...
(a + b) / a - b means $\displaystyle \frac{a+b}{a}-b$ and a+b/(a-b) means $\displaystyle a+\frac{b}{a-b}$.

 

[Love21]

Re: Operation with arrows

I'm sorry, you're right i wasn't clear
this is what I mean

a (arrow) b = (a + b) / ( a - b )
Is that better?

 

[Loren]

1?2 = $\displaystyle \frac{1+2}{1-2}$

2?x = $\displaystyle \frac{2+x}{2-x}$

Can you go from here?

 

[Love21]

Yes, thank you!!