Adding Rational Expressions with Different Denominators

[NoGoodAtMath]

I'm having a bit of trouble with a problem. If anyone can help me, I'd appreciate it. 4w/wsquared+2w-3 +2/1-w

 

[HallsofIvy]

I'm having a bit of trouble with a problem. If anyone can help me, I'd appreciate it. 4w/wsquared+2w-3 +2/1-w

What you have written is extremely ambiguous- without parentheses it is impossible to tell where different denonators end and numerators begin. I think you mean 4w/(w^2+ 2w- 3)+ 2/(1- w).

You should remember from arithmetic with fractions that, to add fractions with different denominators you need to get a "common denominator" by multiplying both numerator and denominator by the same thing. And we can get the "least common denominator" by checking factor. The denominator of the second fraction is 1- w which cannot be reduce (but can be written as -(w- 1). If the other denominator, w^2+ 2w- 1 is to have w-1 as a factor to get that "-3" the other factor would have to be w+ 3: checking(w+ 3)(w- 1)= w^2+ 3w- w- 3= w^2+ 2w- 3. Yes, that is the denominator of the first fraction.

So we can write this as \(\displaystyle \frac{4w}{w^2+ 2w- 3}+ \frac{2}{1- w}= \frac{4w}{(w- 1)(w+ 3)}- \frac{2(w+ 3}{(w-1)(w+ 3)}= \frac{4w- 2w- 6}{(w- 1)(w+ 3)}\)

 

[NoGoodAtMath]

What you have written is extremely ambiguous- without parentheses it is impossible to tell where different denonators end and numerators begin. I think you mean 4w/(w^2+ 2w- 3)+ 2/(1- w).

You should remember from arithmetic with fractions that, to add fractions with different denominators you need to get a "common denominator" by multiplying both numerator and denominator by the same thing. And we can get the "least common denominator" by checking factor. The denominator of the second fraction is 1- w which cannot be reduce (but can be written as -(w- 1). If the other denominator, w^2+ 2w- 1 is to have w-1 as a factor to get that "-3" the other factor would have to be w+ 3: checking(w+ 3)(w- 1)= w^2+ 3w- w- 3= w^2+ 2w- 3. Yes, that is the denominator of the first fraction.

So we can write this as \(\displaystyle \frac{4w}{w^2+ 2w- 3}+ \frac{2}{1- w}= \frac{4w}{(w- 1)(w+ 3)}- \frac{2(w+ 3}{(w-1)(w+ 3)}= \frac{4w- 2w- 6}{(w- 1)(w+ 3)}\)

Hey thanks alot. This is my first time here so I don't know how to write out the expression like you did. But thanks a bunch for replying so quickly. I have a final soon an needed this to be answered. Again thanks for taking the time to answer my post. You're awesome!