Rational Algebraic Fraction Practice Set

Rational Algebraic Fraction [2 Marks]

$1. Simplify: \frac{x}{x-y}+\frac{y}{x+y}-\frac{2xy}{x^{2}-y^{2}}$

$2. Simplify: \frac{a^{2}}{a-b}+\frac{b^{2}}{b-a}$

$3. Simplify: \frac{p+3}{p-2}+\frac{p+2}{p-3}$

$4. Simplify: \frac{x}{x^{2}+3x+2}-\frac{2}{x^{2}-1}$

$5. Simplify: \frac{a+2}{a^{2}+2}-\frac{3}{a^{2}-a-2}$

$6. Simplify: \frac{4}{a^{2}+3a+2}+\frac{2}{a^{2}-1}$

$7. Simplify: \frac{a^{2}-6a+9}{a^{2}}+\frac{a^{2}-5a+6}{a^{2}-a-2}$

$8. Simplify: \frac{a-1}{a^{2}}+\frac{a-2}{a^{2}-5a+6}$

$9. Simplify: \frac{2x-8}{x+3}-\frac{x^{2}+2x-24}{x^{2}-x-12}$

$10. Simplify: \frac{1}{(p-4)(p-5)}+\frac{1}{(p-3)(p-4)}+\frac{1}{(p-3)(p-5)}$

Answers:

1. 1

2. (a + b)

3. -5

4. x²-3x-4 / (x+1)(x-1)(x+2)

5. a²-4 / a(a+1)(a-2)

6. 2(a-1) / (a+2)

7. 1 / a+2

8. 2a-5 / (a-2)(a-3)

9. 3x-14 / x+3

10. 3 / (p-3)(p-5)