Algebra 1 help?

Question

I need help with the Algebra 1 question:

solve:

(This is the best i can do to make fractions, excuse the dots)

a+2 .....a+3
------ + ------ = 5
2a..........a

or:

(a+2)/2a+(a+3)/a=5

(please explain how to solve the problem, please. answer does not need to be included in answer, just an explanation)Thanks

Answer 1

Get a common denominator for all three terms so that they all cancel out, then solve.

a+2+ 2(a+3)=5(2a)

a+2+2a+6=10a

3a+8=10a

-7a=-8

a=8/7

Answer 2

First take the L C M of the denominators
which is 2a then simplify
{ (a+2) + 2(a+3) }/2a = 5 then on simplification
(a+2) + (2a+6) = 10a
3a +8 = 10a
7a = 8
a= 8/7

Answer 3

The first thing you have to do is to make a "common denominator". To do this, you look at the two denominators, and notice that one is "2a" and the other is "a". To make them "common" (or the same), you need to multiply the second one by "2 / 2" (which is equal to 1).

(a+2)/2a + 2(a+3)/2a = 5

Now, you can add the numerators:

[(a + 2) + 2(a + 3)] / 2a = 5

[(a + 2) + (2a + 6)] / 2a = 5

(3a + 8) / 2a = 5

3a + 8 = 10a { Multiplied both sides by "2a" }

8 = 7a

a = 8/7

Answer 4

(a+2)/2a+(a+3)/a=5

you need a common denominator between a and 2a. It will be 2a.

so the second fraction would be 2 (a+3)/2a

then you add using common denominator, so:

(a+2)/2a+2(a+3)/2a= (a+2+2a+6)/2a= (3a+8)/2a

this is the simplified version, which according to the problem is equal to 5 so

(3a+8)/2a = 5 =>> 3a+8 = 10a =>>
8=7a =>>
a=8/7

Answer 5

Clear it of fractions by multipyling each term by 2a
a+2 +2(a+3)=10a
combine like terms
a+2 + 2a +6 = 10a
3a+8 = 10a
subtract 3a from both sides
8=7a
8/7=a

Answer 6

1st make everything into a fraction which includes the 5 into 5/1. Then multiply everything so it has a common denominator of 2a. Then cancel like terms and solve.

a+2 (2)a+3 5(2a)
------ + ---------- = -----------
2a (2) a 1 (2a)


a+2+2a+6 10a
--------------- = ----------
2a 2a

a+2+6= 5 >>>>>>> a+8=5

a= -3

Answer 7

The fractions should be done away with and this can easily be done by multiplying all terms by 2a. After doing this you will have terms including "a" and others that are just numbers. Put all the terms wih "a" on one side of the equation and the numbers on the other side and then solve for "a". I have not worked this out in detail nor included the answer since I assume you want to do this yourself.

Answer 8

(a+2)/2a + (a+3)/a = 5
(a+2)/2a + 2(a+3)/2a = (2a*5)/2a
(a+2) + 2(a+3) = 10a
a + 2 + 2a + 6 = 10a
8 = 10a - 3a
8 = 7a
a = 8/7