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

1 like 0 dislike
36 views
Simplify:
$$\frac{x-2}{x^{2}-4}+\frac{x^{2}}{x-2}-\frac{x^{3}+x-4}{x^{2}-4}, \quad(x \neq \pm 2)$$
| 36 views

0 like 0 dislike
Step 1: Factorise the denominators
$$\frac{x-2}{(x+2)(x-2)}+\frac{x^{2}}{x-2}-\frac{x^{3}+x-4}{(x+2)(x-2)}$$
Step 2: Make all denominators the same so that we can add or subtract the fractions
The lowest common denominator is $(x-2)(x+2)$.
$$\frac{x-2}{(x+2)(x-2)}+\frac{\left(x^{2}\right)(x+2)}{(x+2)(x-2)}-\frac{x^{3}+x-4}{(x+2)(x-2)}$$
Step 3: Write as one fraction
$$\frac{x-2+\left(x^{2}\right)(x+2)-\left(x^{3}+x-4\right)}{(x+2)(x-2)}$$
Step 4: Simplify
$$\frac{x-2+x^{3}+2 x^{2}-x^{3}-x+4}{(x+2)(x-2)}=\frac{2 x^{2}+2}{(x+2)(x-2)}$$
Step 5: Take out the common factor and write the final answer
$$\frac{2\left(x^{2}+1\right)}{(x+2)(x-2)}$$
by Gold Status (13,125 points)

1 like 0 dislike
1 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
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
1 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
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
1 like 0 dislike