Note: dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
In some cases of simplifying an algebraic expression, the expression will be a fraction. For example,
\[\frac{x^{2} + 3x}{x + 3}\]
has a quadratic binomial in the numerator and a linear binomial in the denominator. We have to apply the different factorisation methods in order to factorise the numerator and the denominator before we can simplify the expression.
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Answer:
Note: dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
In some cases of simplifying an algebraic expression, the expression will be a fraction. For example,
\[\frac{x^{2} + 3x}{x + 3}\]
has a quadratic binomial in the numerator and a linear binomial in the denominator. We have to apply the different factorisation methods in order to factorise the numerator and the denominator before we can simplify the expression.
\begin{align*} \frac{{x}^{2} + 3x}{x + 3} & = \frac{x\left(x + 3\right)}{x + 3}\\ & =x \qquad \qquad \left(x\ne -3\right) \end{align*}
If \(x=-3\) then the denominator, \(x + 3 = 0\) and the fraction is undefined.
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