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3 Answers

8 / (1 - x^2) + 5 / (x + 1) = 4 / (x - 1)

-8 / (x^2 - 1) + 5 / (x + 1) = 4 / (x - 1)

-8 /((x + 1)(x - 1)) + 5 / (x + 1) = 4 / (x - 1)

Can’t divide by zero, so x ≠ ± 1.

Multiply both sides by (x + 1)(x - 1):

-8 + 5(x - 1) = 4(x + 1)

-8 + 5x - 5 = 4x + 4

Add -4x + 13 to both sides:

x = 17

check:

8 / (1 - (17)^2) + 5 / ((17) + 1) =? 4 / ((17) - 1)

8/((1 + 17)(1 - 17)) + 5/18 =? 4/16

8/((18)(-16)) + 5/18 =? 1/4

-1/((18)(2)) + 2*5/(2*18) =? 1/4

9/(2*18) = 1/4 √
Hi Mondrea;
I believe Kay's interpretation is correct.  Please let me know if we are mistaken.
8/1-x^2+5/x+1= 4/x-1
[8/(1-x2)]+[5/(x+1)]=4/(x-1)
[8/(1-x2)]+[5/(x+1)]=4/(x-1)
(1-x2)=(1+x)(1-x)
Let's take [5/(x+1)], and multiply it by (1-x)/(1-x) such that the denominator is also (1-x2)
[8/(1+x)(1-x)]+[5(1-x)/(1+x)(1-x)]=4/(x-1)
On the left side, the denominators are identical.  Let's add these together...
[8+5(1-x)]/[(1-x)(1+x)]=4/(x-1)
8+5(1-x)=8+5-5x=13-5x
On the right side, let's multiply the numerator and denominator by -1/-1...
(13-5x)/[(1+x)(1-x)]=[4/(x-1)](-1/-1)
(13-5x)/[(1+x)(1-x)]=-4/(1-x)
(1-x) is now in the denominator of both sides.  It cancels...
(13-5x)/(1+x)=-4
Cross-multiply...
13-5x=-4(1+x)
13-5x=-4-4x
13-5x=-4-4x
Add 4 to both sides...
4+13-5x=-4-4x+4
17-5x=-4x
Add 5x to both sides...
5x+17-5x=-4x+5x
17=x
 
Let's check our work with the original equation...
[8/(1-x^2)]+[5/(x+1)]= 4/(x-1)
[8/(1-172)]+[5/(17+1)]=4/(17-1)
[8/(1-289)]+[5/(17+1)]=4/(17-1)
(8/-288)+(5/18)=4/16
(-8/288)+(5/18)=4/16
(-1/36)+(5/18)=1/4
Let's multiply (5/18) by (2/2)=10/36
Let's multiply (1/4)(9/9)=9/36
(-1/36)+(10/36)=9/36
9/36=9/36
 
 
 
 
 
8/(1-x2)    + 5/(x+1)  = 4/(x-1)
 
8/(1-x)(1+ x)     + 5/(x+1)  = 4/(x-1)
 
multiply both sides with (1+x)(x-1)
 
-8 + 5(x-1)  = 4(x+1)(-1)
 
-8 + 5x - 5 = -4x - 4
 
9x = 9
 
x = 1

Comments

Hi Amarjeet;
x cannot equal 1.  On the right side of the equation, (x-1) is a denominator...  1-1=0.

Comment