Hi Dalia;
(1/x+1)+(a/x^{2}1)=(x/x^{2}1)
I think this is...
[1/(x+1)]+[a/(x^{2}1)]=[x/(x^{2}1)]
Let's combine like terms.
Let's move the second parenthetical equation to the right side. It is currently positive. It will become negative...
[1/(x+1)]=[a/(x^{2}1)]+[x/(x^{2}1)]
Let's consider the fact that...
(x^{2}1)=(x+1)(x1)
Let's do such replacement...
1/(x+1)={a/[(x+1)(x1)]}+x/[(x+1)(x1)]
On the right side, let's combine numerators...
1/(x+1)=(a+x)/[(x+1)(x1)]
(x+1) is in the denominators of both sides. It cancels...
1/(x+1)=(a+x)/[(x+1)(x1)]
1=(a+x)/(x1)
1/1=(a+x)/(x1)
I converted 1 into 1/1 to illustrate my next point.
Let's crossmultiply...
a+x=x1
x on both sides cancels...
a=1
Let's multiply both sides by 1...
(1)(a)=(1)(1)
a=1
Feb 4

Vivian L.