Question 64614
QUESTION:


Given f(x)=1/x and g(x)=(x+1)/(x-2), find f(x)/ g(x) and state its domain.


ANSWER:



f(x)/ g(x) = (1/x )/ ((x+1)/(x-2))


While dividing two rational expressions, take the reciprocal of the divisor(that is f(x)) and multiply it with the divident ( that is g(x) )


==> f(x)/ g(x) = (1/x )*  [(x-2)/(x+1)]


==>            = [ 1 * (x-2)]/[x * (x+1)]



==>            = (x-2)/( x*x - x*1)


==>   f(x)/ g(x) = ( x-2)/(x^2 -x )



OR we can write, f(x)/ g(x) = (x-2)/x(x + 1)



In the denominator, we have x(x + 1)


The values,  x = 0  and x = -1 make the denominator zero.


That means for values, x = 0, -1 the function is not defined.


So we can say that domain of f(x)/ g(x) is set of all real numbers except 0 and -1


That is Domain = R - {0, -1}




Hope you understood.


Regards.


Praseena.