15.3 Operations with algebraic fractions — Practise

1. Simplify $\frac{3}{x}+\frac{2}{x}$.

Answer: $\frac{5}{x}$, $x\neq0$

2. Simplify $\frac{2}{x}+\frac{3}{x+1}$.

Answer: $\frac{5x+2}{x(x+1)}$, $x\neq0,-1$

3. Simplify $\frac{5}{x-1}-\frac{2}{x+1}$.

Answer: $\frac{3x+7}{(x-1)(x+1)}$, $x\neq1,-1$

4. Simplify $\frac{2x}{3}\times\frac{9}{4x}$.

Answer: $\frac{3}{2}$, $x\neq0$

5. Simplify $\frac{x}{3}\div\frac{2x}{5}$.

Answer: $\frac{5}{6}$, $x\neq0$

6. Simplify $\frac{1}{x}+\frac{1}{x+2}$.

Answer: $\frac{2x+2}{x(x+2)}$, $x\neq0,-2$

7. Simplify $\frac{3}{x-2}-\frac{1}{x}$.

Answer: $\frac{2x+2}{x(x-2)}$, $x\neq0,2$

8. Simplify $\frac{x^2-9}{x+3}\times\frac{2}{x}$.

Answer: $\frac{2(x-3)}{x}$, $x\neq0,-3$

9. Simplify $\frac{x+1}{x}\div\frac{x^2-1}{2x}$.

Answer: $\frac{2}{x-1}$, $x\neq0,1,-1$

10. Simplify $\frac{1}{x}+\frac{1}{x^2}$, where $x\neq0$.

Answer: $\frac{x+1}{x^2}$