Algebraic Fractions Practice Worksheet

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📚 Part 1: Add & Subtract — Simplify (show working)

1. Simplify: (x)/(x-2) + 2/(x-2).

2. Simplify: 2x/(x^2-4) + 3/(x+2). (Hint: x^2-4=(x-2)(x+2))

3. Simplify: (x+1)/(x+3) − 2/(x+3).

4. Simplify and state any restrictions: 3/(x^2-9) − 1/(x-3). (x^2-9=(x-3)(x+3))

5. Add: 2x/(x-1) + 3/(x(x-1)).

6. Simplify: (x+2)/x + 4/x.

7. Simplify: x/(x+1) + 1/(x+1)^2. State values of x that must be excluded.

8. Simplify: (x+2)/(x-1) × (x-1)/(x+3).

9. Simplify: (3x)/4 × 8/(6x).

10. Simplify: (x^2−1)/(x+1) ÷ (x-1)/x. (Factor where helpful.)

11. Simplify: 2x/(x+4) ÷ 6/(x(x+4)).

12. Simplify: (3x^2)/5 × 10/(9x).

13. Simplify: (x+5)/(x^2−25) × (x−5)/2. (x^2−25=(x−5)(x+5))

14. Simplify the complex fraction: ( x/(x+1) ) ÷ ( 1/(x+1) ).

15. Simplify: ( (x+2)/x ) ÷ ( (x+2)/x^2 ).

16. Simplify and give any restrictions: (1/x + 1/(x+1)) ÷ (1/x − 1/(x+1)).

17. Solve for x, stating any excluded values: x/(x-2) = 3/(x-2).

18. Solve for x: (x+1)/x = 3. State any excluded values.

19. Simplify: (x^2+2x)/x ÷ (x+2).

20. Simplify: 1/(x-1) + 1/(x+1). Combine into a single simplified fraction and state restrictions.