Sites: Global Q&A | Wits | MathsGee Club | Joburg Libraries | StartUps | Zimbabwe | OER

MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
52 views
Simplify: $\dfrac{x-2}{{x}^{2}-4}+\dfrac{{x}^{2}}{x-2}-\dfrac{{x}^{3}+x-4}{{x}^{2}-4}, ~~(x \neq \pm2)$.
| 52 views

0 like 0 dislike

Simplifying fractions

Simplify: $\dfrac{x-2}{{x}^{2}-4}+\dfrac{{x}^{2}}{x-2}-\dfrac{{x}^{3}+x-4}{{x}^{2}-4}, ~~(x \neq \pm2)$.

Step 1 - Factorise the denominators
$\begin{equation*} \frac{x-2}{(x+2)(x-2)}+\frac{{x}^{2}}{x-2}-\frac{{x}^{3}+x-4}{(x+2)(x-2)} \end{equation*}$

Step 2 - Make all denominators the same so that we can add or subtract the fractions - The lowest common denominator is $(x-2)(x+2)$.

$\begin{equation*} \frac{x-2}{(x+2)(x-2)}+\frac{({x}^{2}) (x+2)}{(x+2)(x-2)}-\frac{{x}^{3}+x-4}{(x+2)(x-2)} \end{equation*}$

Step 3 - Write as one fraction
$\begin{equation*} \frac{x-2+({x}^{2})(x+2)-(x^{3}+x-4)}{(x+2)(x-2)} \end{equation*}$

Step 4 - Simplify

$\begin{equation*} \dfrac{x-2+{x}^{3}+ 2x^{2}-x^{3} - x+4}{(x+2)(x-2)} = \dfrac{2x^{2} + 2}{(x+2)(x-2)} \end{equation*}$

Step 5 - Take out the common factor and write the final answer

$\begin{equation*} \dfrac{2({x}^{2} +1)}{(x+2)(x-2)} \end{equation*}$

by Diamond (89,356 points)

0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
0 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike