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# Excluded Values for Rational Expressions

## Key Questions

• The only rule with rational expression is that the denominator can't be zero, since you can't divide by zero.

Remember that an expression is said to be rational only if variables appear at the denominator: thus $\setminus \frac{\setminus \cos \left(x\right) + 3 {x}^{2}}{2}$ is NOT a rational expression.

If you actually have an expression in which variables appear at the denominator, you must exclude the values of the variables for which the expression at the denominator becomes 0. In formulas, if you have an expression like $\setminus \frac{f \left(x\right)}{g \left(x\right)}$, such an expression is defined for all $x$ such that $g \left(x\right) \setminus \ne 0$.

• They are all values that make the denominator zero.

I hope that this was helpful.

Explanation is below

#### Explanation:

In order to simplify a rational expression, we factorize the numerator & denominator both. Then cancel out the factors which are common in both numerator & denominator. Thus we get a simplified rational expression.

See below

#### Explanation:

Let our general rational expression be $f \frac{x}{g} \left(x\right)$

This expression is defined where $g \left(x\right) \ne 0$
[Since we cannot divide by 0]

Hence, the excluded values are where $g \left(x\right) = 0$

Hope this helps!