Question

Simplify the following rational expression

5k? - 50k +45
k2 - 18k + 81
Which values of k make the expression undefined?
Choose all answers that apply:

Answer 1

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

Explanation:

Given as :

The rational expression is written in the form

`(5k^(2)-50k+45)/(k^(2)-18k+81)`

Now, according to question

The expression to be undefined , denominator should be 0

As,
`(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