A little help would be appreciated...?

Question

Now I am not a math person, I'm an English person, so i already have a tad difficulty with math. Anyway, over the summer,w hat little skills I had became rusty  and I am just seeking for a little help.

To Solve

4 + 6 +=      15
----  ----     ----------
x-1  3x+1    3x+1

I know you need to multiply by the LCD and go from there, but after that I am little lost. SO if you could just help me please. thanks

Captain Mephisto · Accepted Answer

I will try to explain in general and then be specific about this problem

1. (N / N) = 1. N can be a number or an expression like x - 1 as long as N is not 0). This is just the mathematical way of saying that something divided by the same thing is just 1.

2. If you have an equation such as N + M = X then you can multiply all terms be the same thing and still have a valid equation.
a*(N + M) = a*X = a*N + a*M

3. You can divide both sides of an equation by the same thing and still have a valid equation.
N + M = X
(N + M)/a = X/a = N/a + M/a

In this type of problem you want to get rid of the fractions and just end up with something like N + M = X.

Take the first term 4/(x - 1) and apply what I said in 2 and 1 above. We can multiply everything by (x - 1) and then use (x - 1)/(x - 1) = 1 to get just 4 for the first term.
(x - 1)*[4/(x - 1) + 6/(3x + 1)] = (x - 1)*15/(3x + 1)
(x - 1)*4/(x - 1) + (x - 1)6/(3x + 1) = (x - 1)*15/(3x + 1)
4 + (x - 1)6/(3x + 1) = (x - 1)*15/(3x + 1)

As you have probably already seen the other two terms both have (3x + 1) for the denominator. Now multiply each side by that expression and use the fact that (3x + 1)/(3x + 1) = 1.
(3x + 1)*[4 + (x - 1)6/(3x + 1)] = (3x + 1)*(x - 1)15/(3x + 1)
(3x + 1)*4 + (3x + 1)(x - 1)6/(3x + 1) = (3x + 1)*(x - 1)15/(3x + 1)
(3x + 1)*4 + (x - 1)6 = (x - 1)15

Combine the two terms in (x - 1)
(3x + 1)4 = (x - 1)15 - (x - 1)6 = (x - 1)9

Now just multiply everything out.
12x + 4 = 9x - 9

And put all x's on one side and the numbers on the other.
12x - 9x = -9 - 4
3x = -13
x = -13/3

And you should always check to make sure an answer is correct. You do this by simply calculating out each term and then adding the two on the left hand side to see if you get what you calculated for the third.
4/(x - 1) = 4/(-13/3 - 1) = 4/(-13/3 - 3/3) = 4/(-16/3) = -3/4
6/(3x + 1) = 6/(-3*13/3 + 1) = 6/(-13 + 1) = 6/(-12) = -18/36 = -1/2
15/(3x + 1) = (15/(-12) = -5/4

Now add the first two and see if we get the third:
-3/4 - 1/2 = -3/4 - 2/4 = -5/4 and that is right

Trending News

A little help would be appreciated...?

1 Answer