Solve. Check the solution. (2/x-1) = (x+4/3)

Question

helpppp pleaseee need answer quick

Answer 1

OK, Robyn, you are still confused by what is being asked.

 

2/(x - 1) = (x+4)/3

 

We are solving for x?  We know that we can cross multiply!

 

2(3) = (x - 1)(x + 4)

 

Multiplying out, we get 6 = x² + 3x - 4

 

If we subtract 6 from both sides, we get 0 = x² + 3x - 10

 

We have to factor x² + 3x - 10 into (x + 5)(x - 2).  Again, you should know how to do that.

 

So, we have (x + 5)(x - 2) = 0

 

In order for the left side to equal 0, then either, or both, of the binomial factors has to equal. So, we set each equal to 0 and solve.

 

x + 5 = 0

     x = -5

 

x - 2 = 0

     x = 2

 

So, our two answers are x = -5 and 2

 

Let's check.

 

2/(-5 - 1) = (-5 + 4)/3

2/-6 = -1/3

-1/3 = -1/3. Check!

 

2/(2-1) = (2+4)/3

2/1 = 6/3

2 = 2. Check!

Answer 2

2/(x-1) = x + 4/3

Let's get rid of the fraction by multiplying through by 3

3(2/(x-1)) = 3(x + 4/3)

6/(x-1) = 3x + 4

Now multiply both sides by (x-1)

6 = (3x+4)(x-1)

6 = 3x² - 3x + 4x -4

6 = 3x² + x -4

Subtract 6 from both sides to get a quadratic

3x² + x - 10 = 0

The product of the first coefficient (3) and the constant (-10) is 3(-10) = -30

Let's see if there are factors of -30 that add to make 1 which is the coefficient of the middle x term

(6)(-5) = -30 and 6-5 = 1

Using 6 and -5 change the x term to 6x - 5x so we can factor the polynomial

3x² + 6x - 5x -10 = 0

Now factor...

3x(x+2) -5(x+2) = 0

(3x-5)(x+2) = 0

 

So either 3x-5 = 0      or    x + 2 = 0

3x = 5                               x = -2

x = 5/3

 

So the answers are x = -2, 5/3

 

check:  x = -2                         check: x = 5/3

2/(-2-1) = -2 + 4/3                 2/(5/3 - 1) = 5/3 + 4/3

-2/3 = -12/6 + 8/6                  2/(2/3) = 9/3

-2/3 = -4/6                             2(3/2) = 3

-2/3 = -2/3                             3 = 3

check... yes                             check ... yes