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-x^{2})]+[5/(x+1)]=4/(x-1)

[8/(1-x^{2})]+[5/(x+1)]=4/(x-1)

(1-x^{2})=(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-x^{2})

[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/(1-17^{2})]+[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

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