Given that f(x)=x+1 and g(x)=1-x solve the inequality f(x)/g(x)>0

f(x)=x+1 and g(x)=1-x. To solve the inequality
f(x)/g(x)>0

Therefore to Let R(x) = f(x)/g(x) =
(x+1)/(x-1) > 0.

R(x) = (x+1)/(x-1) >
0.

When x > 1, R(x) > 0, as both numerator
x+1) > 0 and  denominator x-1> 0 .

When  when
x = 1, R(x) = (x+1)/(x-1) is not defined as denominator x-1 =
0.

When -1 < x< 1,  numerator  is positive
and denominator  negative. So R(x) = (x+1)/(x-1) <
0.

When x= -1, both numerator = 0. Denominator = -2. So
R(x) = (x+1)/(x-1) = 0.

When x< -1, both numerator
and denominator are negative. So R(x) = (+1)/(x-1) >
0.

Therefore f(x)/g(x) = (x+1)/(x-1) > 0
.only when  x< -1  OR when x >
1.