91Ó°ÊÓ

Consider the expression.

$x+\left(-\frac{11}{12}\right)$

Substitute $\frac{11}{12}$for $x$into the given expression.

localid="1647945238402" $x+\left(-\frac{11}{12}\right)=\frac{11}{12}+\left(-\frac{11}{12}\right)$

Conclude that the fractions have the same denominators .

Therefore, add the fractions to simplify the expression.

localid="1647943694286" $\begin{array}{rcl}x+\left(-\frac{11}{12}\right)& =& \frac{11+(-11)}{12}\\ & =& 0\end{array}$

Thus, the value of the expression when $x=\frac{11}{12}$is $0$.

Substitute $\frac{3}{4}$for $x$into the given expression.

width="180">x+-1112=34+-1112

Conclude that the fractions have different denominators.

So, find the least common denominator of $4$and $12$.

$\begin{array}{rcl}4& =& 2·2\\ 12& =& 2·2·3\\ & ⇒& LCM=2·2·3\\ & ⇒& LCM=12\end{array}$

Rewrite as equivalent fractions with the least common denominator, $12$.

$\begin{array}{rcl}x+\left(-\frac{11}{12}\right)& =& \frac{3}{4}·\frac{3}{3}+\left(-\frac{11}{12}\right)·\frac{1}{1}\end{array}$

Simplify.

$\begin{array}{rcl}x+\left(-\frac{11}{12}\right)& =& \frac{9}{12}+\left(-\frac{11}{12}\right)\end{array}$

Add the fractions to simplify the expression.

$\begin{array}{rcl}x+\left(-\frac{11}{12}\right)& =& \frac{9+(-11)}{12}\\ & =& \frac{-2}{12}\\ & =& -\frac{1}{6}\end{array}$

Hence, the value of the given expression when $x=\frac{3}{4}$is $-\frac{1}{6}$.