Name: Comparing Fractions
Uploaded: 2019-07-19
Duration: 10 min 22 s
Description: This video discusses the approach of converting fractions into decimals and arranging the given fractions in ascending and descending order.

Question

Show that

\frac{x^{2} - 9}{x + 3}

simplifies to

x - 3

. Use your GDC or graphing software to draw the graphs of both expressions. Describe any similarities or differences between the graphs.

Accepted Answer

Consider

$\frac{x^{2} - 9}{x + 3}$

$= \frac{(x - 3) (x + 3)}{(x + 3)}$ [Factorizing the numerator]

$= x - 3$ [Cancelling the common factors in the numerator and denominator]

Now, we know that the graph of $\frac{x^{2} - 9}{x + 3}$ is a straight line joining the points $(0, - 3),$ and $(3, 0)$ but it is not defined at point $x = - 3$ whereas the graph of $y = x - 3$ is also a straight line defined for all real numbers.

Thus, the graphs of both the functions are given as follows:

And, the graph of $y = x - 3$ is given as follows:

Thus, the similarities between the above two graphs is that the graph of both the functions is a straight line. and both intersect the $x$ -axis at $(3, 0)$ and $y$ -axis at $(0, - 3)$ . The difference between the two graphs can be stated in terms of its continuity, domain and range.

From the graph, the function $y = \frac{x^{2} - 9}{x + 3}$ is continuous everywhere except at point $x = - 3$ . And, the function $y = x - 3$ is continuous at all real numbers.

The domain of the function $y = \frac{x^{2} - 9}{x + 3}$ is $x \in R - \{3\}$ . And, the domain of the function $y = x - 3$ is $x \in R$ .

The range of the function $y = \frac{x^{2} - 9}{x + 3}$ is $(- \infty, - 6) \cup (- 6, \infty)$ . And, the range of the function $y = x - 3$ is $(- \infty, \infty)$ .

Show that $\frac{x^{2} - 9}{x + 3}$ simplifies to $x - 3$ . Use your GDC or graphing software to draw the graphs of both expressions. Describe any similarities or differences between the graphs.

Important Questions on Rational Algebraic Expressions

Learn and Prepare for any exam you want !

Show that x2-9x+3 simplifies to x-3. Use your GDC or graphing software to draw the graphs of both expressions. Describe any similarities or differences between the graphs.

Important Questions on Rational Algebraic Expressions

Learn and Prepare for any exam you want !

Show that $\frac{x^{2} - 9}{x + 3}$ simplifies to $x - 3$ . Use your GDC or graphing software to draw the graphs of both expressions. Describe any similarities or differences between the graphs.