Question

Find the nonpermissible replacement for y inthis expression.(y +3)/(y-1)

Answer 1

To find the nonpermissible replacement for y in the expression;

$\frac{y+3}{y-1}$

The nonpermissible replacement for y is the replacement for y at which the denominator of the expression is zero. (when the denomenator is zero, the final value can not be determined).

For the given expression, the denomenator is;

$y-1$

For y to be nonpermissible, the denometor must be equal to zero.

$y-1=0$

To get y, add 1 to both sides.

$\begin{gathered} y-1+1=0+1 \\ y=1 \end{gathered}$

At y =1, the expression becomes;

$\frac{y+3}{y-1}=\frac{1+3}{1-1}=\frac{4}{0}\rightarrow\text{ nonpermissible }$

Therefore, the nonpermissible replacement for y in the given expression is;

$y=1$