Algebra Help

Guffrey

So, I'm back in school for geology after completing my associate's in criminal justice right out of high school. I'm taking my first chemistry class ever, and its assuming a knowledge of college algebra. I'm in Calc 1 now, and got an A in algebra back in the day, but I'm having trouble getting back into the swing of things. Here is the first problem I've been given.

Solve for x:

(3/(2+x)) + (1/(3+x))=15

Now, I'm assuming that I would first multiply each numerator by its denominator, giving me:

3(2+x)+1(3+x)=15 the denominators getting canceled out in the process

so then 6+3x+3+x=15

4x+9=15

4x=6

x=6/4, reduced to 3/2

Did I totally do this wrong?


EDIT: Just noticed I think he wanted it as 15., not 15 The decimal point gets into the territory of significant digits, so I'm pretty sure I did this wrong. The syllabus says all solutions to assigned problems will be posted in a case outside our lab, so I'm hoping to go there on Monday (due Tuesday) and get the answers so I can work it through that way.

SeñorAmor

You're on the right track with multiplying by the denominator to remove the variables in the denominator, but you have to multiply the whole side by an appropriate value to cancel both out. In this case, you can't simply multiply by (2+x) for the first fraction and (3+x) for the second. What you need to do is multiply the whole left side by something that will cancel out BOTH the (2+x) and (3+x). Keep in mind whatever you multiply the left side by, you'll need to do the exact same thing to the right side. If you multiply the left side by 10, you have to do the same to the right side.

I don't want to do your work for you, so I'll stop here until you have more specific questions or get further along in this problem.

Clipse

Your first step is not correct, and I'm not sure what the reasoning behind it is. A correct and common strategy here would be to multiply the whole equation by the least common denominator -- in this case,

(2+x)*(3+x)

. That gives you

3*(3+x) + 1*(2+x) = 15*(2+x)*(3+x)

. When you

expand this and put all the terms on one side

, you'll have a

quadratic equation, and you can just solve it with the quadratic formula

.

Edit: Spoilered stuff to avoid giving the whole answer. Each spoiler reveals more of the answer in order, so read them at your own discretion. Hope I wasn't too late with this edit.

SeñorAmor

Sigh. Welp, so much for not doing the work for him.

Demerdar

SeñorAmor wrote:

You're on the right track with multiplying by the denominator to remove the variables in the denominator, but you have to multiply the whole side by an appropriate value to cancel both out. In this case, you can't simply multiply by (2+x) for the first fraction and (3+x) for the second. What you need to do is multiply the whole left side by something that will cancel out BOTH the (2+x) and (3+x). Keep in mind whatever you multiply the left side by, you'll need to do the exact same thing to the right side. If you multiply the left side by 10, you have to do the same to the right side.

I don't want to do your work for you, so I'll stop here until you have more specific questions or get further along in this problem.

Pretty much this.

Guffrey

Thank you all for your help. Clipse, I haven't checked out your spoilers yet, but I appreciate you putting them like that. I'd really like to do it all myself, since I'll need to be able to do it on the exam. I figured I needed to do the same on the other side, thats a basic fact of algebra I overlooked at first. These first weeks are always frustrating. I'm honestly not sure I could of done great on the optional "algebra assessment" we had in trig last semester, yet I ended up doing fine in the class (high . These beginning reviews always kill me till I get back in my math groove. Thanks again everyone.