Is ab+ac/a equal to b+ac? AB+AC/A=B+AC Equality Homework"

[Cornraker]

Homework Statement

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?

 

[Borek]

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

or

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

?

 

[Cornraker]

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

 

[Mark44]

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

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.

 

[dacruick]

either way they arent equal. so what does it matter

 

[Mark44]

either way they arent equal. so what does it matter

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

 

[dacruick]

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

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?

 

[Char. Limit]

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.

 

[Mark44]

But it doesn't matter with respect to his answer.

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.

Neither of them are equal. If the problem represented something physical then i understand that.'

I don't see how that makes a difference.

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

So are you saying that it is not better to know exactly what the problem is?

 

[Cornraker]

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.

 

[Mark44]

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

 

[dacruick]

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