# Dividing out a variable from a quotient

• Oct 29th 2012, 06:55 AM
AZach
Dividing out a variable from a quotient
I don't think I've ever mastered this concept. If I have a problem like $\displaystyle \frac{x+2a+3b}{x} = {4}$, can I just divide the x out to get $\displaystyle 1+2a+3b = 4$ ?

I know if I look at the first expression like $\displaystyle \frac{x}{x} + \frac{2a}{x} + \frac{3b}{x}$ then I could turn x/x into 1, but the expression would look like $\displaystyle 1 + \frac{2a}{x} + \frac{3b}{x}$. The x could get brought back into the quotient if it had a common denominator.

Also, if the sample problem were $\displaystyle \frac{x*2b+a}{x}$ would that make a difference in mathematical rules for dividing out the x? (As opposed to addition or subtraction).

I hope my question makes sense, if not I can explain more.
• Oct 29th 2012, 07:07 AM
richard1234
Re: Dividing out a variable from a quotient
Quote:

Originally Posted by AZach
I don't think I've ever mastered this concept. If I have a problem like $\displaystyle \frac{x+2a+3b}{x} = {4}$, can I just divide the x out to get $\displaystyle 1+2a+3b = 4$ ?

No. x is not a factor of the top; you cannot simply cancel out the x.

The correct simplification is $\displaystyle 1 + \frac{2a}{x} + \frac{3b}{x} = 4$, as you did, or alternatively, $\displaystyle 1 + \frac{2a+3b}{x} = 4$.