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# Manipulating Rational Expressions

## Manipulating Rational Expressions 1.11 - Solution

a
By substituting $x=8$ into the rational expression we can find $R(8)$.
$R(x)=\dfrac{x+7}{x-7}$
$R({\color{#0000FF}{8}})=\dfrac{{\color{#0000FF}{8}}+7}{{\color{#0000FF}{8}}-7}$
$R(8)=\dfrac{15}{1}$
$R(8)=15$
For $x=8$, the rational expression has the value $15$.
b
The rational expression is undefined when the denominator equals zero, since division by zero is not allowed. The denominator is $x-7$, so the $x$-value that makes the denominator become equal $0$ must be $7$. We can justify this algebraically by setting the denominator equal to $0$ and solve for $x$.
$x-7=0$
$x=7$
c
Multiply both the numerator and the denominator by $7$.
$R(x)=\dfrac{x+7}{x-7}$
$R(x)=\dfrac{(x+7)\cdot 7}{(x-7)\cdot 7}$
$R(x)=\dfrac{x\cdot 7+7\cdot 7}{x\cdot 7-7\cdot 7}$
$R(x)=\dfrac{7x+49}{7x-49}$