SOLUTION: Hi I need help with adding and subtracting with unlike denominators. If you can do these 3 problems and try to explain how you did them I would be very appreicative. 1. (x+8)/

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi I need help with adding and subtracting with unlike denominators. If you can do these 3 problems and try to explain how you did them I would be very appreicative. 1. (x+8)/      Log On


   

Question 74431: Hi I need help with adding and subtracting with unlike denominators. If you can do these 3 problems and try to explain how you did them I would be very appreicative.
1. (x+8)/(3x-1) + (x+3)/(x+1)
2. 4/(x+4) - 7/5x
3. 4x/(5x-2) - 2x/(5x+1)
Thank You!
Found 2 solutions by jim_thompson5910, cathieb1225:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
When we add fractions with different denominators we have to make them the same so we can add them. For instance 1%2F2%2B1%2F3 cannot be added unless we have similar denominators. To make them have like denominators, we have to find a common number that they can multiply to. 2 and 3 can both multiply to 6 (for instance 2*3=6 and 3*2=6). Since they're both at 6 we can now add them. In other words this happens
Notice how we multiplied each term by a form of 1 (2/2 and 3/3) so they didn't change. So to find the common denominator we multiply the 2 denominators.
This same idea applies to unknown variables.



1.
The common denominator is:
(x+1)(3x-1) we can leave it as it is. We don't need to foil.
%28x%2B8%29%2F%283x-1%29+%2B+%28x%2B3%29%2F%28x%2B1%29Start with the given problem
Multiply the first term by %28x%2B1%29%2F%28x%2B1%29 which is a clever form of 1 to get to the common denominator. Multiply the second term by %283x-1%29%2F%283x-1%29 which is a clever form of 1 to get to the common denominator.
Since they have similar denominators, we can add now.
%28%28x%2B1%29%28x%2B8%29%2B%283x-1%29%28x%2B3%29%29%2F%28%28x%2B1%29%283x-1%29%29
%28x%5E2%2B9x%2B8%2B3x%5E2%2B8x-3%29%2F%28%28x%2B1%29%283x-1%29%29which foils to this
%284x%5E2%2B17x%2B5%29%2F%28%28x%2B1%29%283x-1%29%29Which simplifies to this




2.The common denominator is (5x)(x+4)
4%2F%28x%2B4%29+-+7%2F5xStart with the given problem
%285x%2F5x%29%284%2F%28x%2B4%29%29+-+%28%28x%2B4%29%2F%28x%2B4%29%29%287%2F5x%29Multiply the first term by %285x%29%2F%285x%29 which is a clever form of 1 to get to the common denominator. Multiply the second term by %28x%2B4%29%2F%28x%2B4%29 which is a clever form of 1 to get to the common denominator.
20x%2F%285x%28x%2B4%29%29+-+%287%28x%2B4%29%29%2F%285x%28x%2B4%29%29
%2820x-7%28x%2B4%29%29%2F%285x%28x%2B4%29%29
%2820x-7x-28%29%2F%285x%28x%2B4%29%29Distribute the 7 to each term
%2813x-28%29%2F%285x%28x%2B4%29%29Simplify




3.The common denominator is (5x-2)(5x+1)
4x%2F%285x-2%29+-+2x%2F%285x%2B1%29Start with the given problem
Multiply the first term by %285x%2B1%29%2F%285x%2B1%29 which is a clever form of 1 to get to the common denominator. Multiply the second term by %285x-2%29%2F%285x-2%29 which is a clever form of 1 to get to the common denominator.


%284x%285x%2B1%29-2x%285x-2%29%29%2F%28%285x%2B1%29%285x-2%29%29
%2820x%5E2%2B4x-10x%5E2%2B4x%29%2F%28%285x%2B1%29%285x-2%29%29Distribute
%2810x%5E2%2B8x%29%2F%28%285x%2B1%29%285x-2%29%29Simplify
Hope this helps.

Answer by cathieb1225(41) About Me  (Show Source):
You can put this solution on YOUR website!
1. (x+8)(3x-1)+(x+3)(x+1)
First, multiply the two binomial sets.
(3x^2-x+24x-8)+(x^2+x+3x+3)
Combine any like terms in the parentheses
(3x^2+23x-8) +(x^2+4x+3)
Drop the parentheses. Because there is an addition sign between the two sets of parentheses, there will be no sign changes in the second set of parentheses.
3x^2+23x-8+x^2+4x+3
Combine like terms
-5x^2+27x-5
To avoid confusion, you can also rewrite the expression with the like terms beside each other.
2. 4/(x+4) - 7/5x
First, you must make both "fractions" have a common denominator. You do this by multiplying the first by 5x/5x and the second by (x+4)/(x+4). That is the same thing as multiplying both of them by 1. This gives you an equivalent fraction for each one of them.
(5x/5x)(4/x+4)-(x+4)/(x+4)(7/5x)
Multiply them out.
(20x/5x^2+20x) - (7x+4/5x^2+20x)
Now that they have a common denominator, you can put the numerators together.
Note that the minus sign between the two fractions causes both the 7x and the 4 to be negative.
20x-7x-4/5x^2+20x
Combine like terms in the numerator.
13x-4/5x^2+20x
3. 4x/(5x-2) - 2x/(5x+1)
You will do the same thing with this expression, giving both fractions a common denominator. This will be done by multiplying the first fraction by (5x+1)/(5x+1) and the second one by (5x-2)/(5x-2).
(5x+1)/(5x+1)(4x/5x-2)-(5x-2)/(5x-2)(2x/5x+1)
Multiply them out.
(20x^2+4x/(25x^2-10x+5x-2)-(10x^2+4)/25x^2-10x+5x-2)
Combine the like terms in the denominators.
(20x^2+4/25x^2-5x-2)-(10x^2+4)/25x^2-5x-2)
Now that they have a common denominator, you can put the numerators together.
Note that the minus sign between the two fractions causes 10x^2 and the 4 to be negative.
20x^2+4x-10x^2-4x/25x^2-5x-2
Combine like terms in the numerator.
10x^2/25x^2-5x-2