Adding and Subtracting Rational Expressions
there are two problems I get stuck with towards the end.
1) 5n/3 + 4n/3
5n+4n/3
9n/3
now i get stuck, i think that I must factor it more but i am unsure, my teacher said I incorrectly distribute the signs?
2) 7/x-5 - 2+x/x-5
for this one I get an answer of -1
1) 5n/3 + 4n/3 = 9n/3
9n/3 = 3n
2)7/(x-5) - (2+x)/(x-5) = (7-2+x)/(x-5)
= (5+x)/(x-5)
To simplify rational expressions, we need to find a common denominator and then combine like terms.
1) 5n/3 + 4n/3:
In this case, the common denominator is 3 because both fractions have a denominator of 3. To combine them, we add the numerators and keep the denominator the same. So we have:
(5n + 4n)/3 = 9n/3
Now, to simplify further, we divide both the numerator and denominator by their greatest common factor, which is 3:
9n/3 = 3n
So the simplified expression is 3n.
It seems like you got stuck because you mistakenly distributed the signs in the numerator. Remember, when adding fractions, you only add the numerators if the denominators are the same.
2) 7/(x-5) - (2+x)/(x-5):
In this case, the common denominator is (x-5) because both fractions have the same denominator. To combine them, we subtract the second fraction from the first one while keeping the denominator the same. So we have:
(7 - (2+x))/(x-5) = (5 + x)/(x-5)
Now, since the numerator and denominator do not have any common factors, this is the simplified expression.
So the final answer is (5 + x)/(x-5).
It seems like you already simplified the expression correctly and got (-1) as the answer. Well done!