Question 237901
1)
For what value of n is{{{(n^3-2n)/(n^2-81)}}} undefined?
The expression is undefined when the denominator is zero, so what value of n would make the denominator equal to zero?
Set the denominator equal to zeor and solve for n.
{{{n^2-81 = 0}}} Add 81 to both sides.
{{{n^2 = 81}}} Take the square root of both sides.
{{{n = 9}}} or {{{n = -9}}}
When n=9 or n=-9, the expression is undefined.
2)
Rationalize the denominator:
{{{(sqrt(x)-sqrt(y))/(sqrt(x)+sqrt(y))}}} Multiply the top and bottom of the fraction by the conjugate of the denominator {{{sqrt(x)-sqrt(y)}}}.
{{{((sqrt(x)-sqrt(y))*(sqrt(x)-sqrt(y)))/((sqrt(x)+sqrt(y))*(sqrt(x)-sqrt(y)))}}} Simplify.
{{{highlight((x-2sqrt(x)sqrt(y)+y)/(x-y))}}}