Math20 help

Question

 

d) Solve 

 

5 over x-1  + 2 over x+1 = -6

 

 

 

then how to check the answer.

 

Answer 1

d) The equation 5/(x - 1) + 2/(x + 1) = - 6

[5(x + 1) + 2(x - 1)]/(x - 1)(x + 1) = - 6

[5x + 5 + 2x - 2]/(x² - 1) = - 6

7x + 3 = - 6(x² - 1)

7x  + 3 = - 6x² + 6

6x² + 7x + 3 - 6 = 0

6x² + 7x - 3 = 0

6x² + 9x - 2x - 3 = 0

3x(2x + 3) - 1(2x + 3) = 0

(2x + 3)(3x - 1) = 0

2x + 3 = 0 and 3x - 1 = 0

2x = - 3 and 3x = 1

x = - 3/2 and x = 1/3

Solutions are x = - 3/2 and x = 1/3.

 

Check :

Substitute the x values in the given equation.

For x = - 3/2,

5/[(- 3/2) - 1) + 2/[(-3/2) + 1] = - 6

5/[(- 3 - 2)/2] + 2/[(- 3 + 2)/2] = - 6

5/[- 5/2] + 2/[(- 1)/2] = - 6

5/[- 5/2] + 2/[(- 1)/2] = - 6

- 2  - 4 = - 6

- 6 = - 6

The statement is true.

For x =  1/3,

5/[(1/3) - 1) + 2/[(1/3) + 1] = - 6

5/[(1 - 3)/3] + 2/[(1 + 3)/3] = - 6

[5/(- 2/3)] + [2/(4/3)] = - 6

(- 15/2) + (3/2) = - 6

( - 15 + 3)/2 = - 6

- 12/2 = - 6

- 6 = - 6

The statement is true.