# Ab+ac/a=b+ac Equality

1. Jan 26, 2010

### Cornraker

1. The problem statement, all variables and given/known data

So i get a home work problem that goes like this. ab+ac/a=b+ac.

is the left side of the equation not equal to or equal to the right side?

2. Jan 26, 2010

### Staff: Mentor

Re: Equality

$$ab + \frac {ac} {a} = b + ac$$

or

$$\frac {ab + ac} {a} = b + ac$$

?

3. Jan 26, 2010

### Cornraker

Re: Equality

thanks Borek. My answers in the back of my textbook say it is not equal but i can't figure out why. ill ask my teacher tommorow i just wanted to get some help ahead of time. thanks

4. Jan 26, 2010

### Staff: Mentor

Re: Equality

Please read what Borek wrote. He's not giving you and answer; he's trying to understand what you meant. Please use parentheses to indicate which expressions are in the numerator on the left side.

5. Jan 26, 2010

### dacruick

Re: Equality

either way they arent equal. so what does it matter

6. Jan 26, 2010

### Staff: Mentor

Re: Equality

It's always better to know exactly what the problem is than to not know, that's why it matters.

7. Jan 26, 2010

### dacruick

Re: Equality

But it doesn't matter with respect to his answer. Neither of them are equal. If the problem represented something physical then i understand that.'

And for the record, you support your statements poorly. Why should i know this? oh because its better to know then not to know?

8. Jan 26, 2010

### Char. Limit

Re: Equality

Well, the second equation is equal when a=1...

And the first equation is equal when a=1 and b=c.

They aren't necessarily unequal.

9. Jan 26, 2010

### Staff: Mentor

Re: Equality

Yes, that is true. On the other hand, a large number of posters in this forum present problems that are ambiguous. For my part, I would rather make these posters aware that their problems can be interpreted in multiple ways than work all possible variants of these problems.
I don't see how that makes a difference.
So are you saying that it is not better to know exactly what the problem is?

10. Jan 26, 2010

### Cornraker

Re: Equality

Ok I looked at it again and I do realize he was just asking which form of the problem I meant and the second one is the correct one. I still do not understand why they are unequal.

11. Jan 26, 2010

### Staff: Mentor

Re: Equality

$$\frac {ab + ac} {a} = \frac{a(b + c)}{a} = b + c \neq b + ac$$
The first and last expressions above are not identically equal. They are conditionally equal for some values of the variables, such as a = 1.

12. Jan 26, 2010

### dacruick

Re: Equality

Cornraker, just because they are equal for some values does not in a sense warrant that equal sign.