Question

Simplify the following rational expression

Answer 1

Answer:

The value of k for the expression to be undefined is 9 .

Step-by-step explanation:

Given as :

The rational expression is written in the form

$\dfrac{5k^{2}-50k+45}{k^{2}-18k+81}$

Now, according to question

The expression to be undefined , denominator should be 0

As, $\frac{1}{0}$ is infinite ( ∞ ) term and it is undefined  , so for expression to be undefined , the denominator should be 0

∴ k² - 18 k + 81 = 0

Or, k² - 9 k - 9 k + 81 = 0

Or, k ( k - 9 ) - 9 ( k - 9) = 0

Or, ( k - 9 ) ( k - 9 ) = 0

Or,  ( k - 9 ) = 0  ,   ( k - 9 ) = 0

∴  k = 9

So, The value of k = 9

Hence The value of k for the expression to be undefined is 9 . Answer