15.2 Simplifying algebraic fractions — Practise

1. Simplify $\frac{x^2-16}{x^2+8x+16}$ and state the excluded value.

Answer: $\frac{x-4}{x+4}$, $x\neq-4$

2. Simplify $\frac{6x^2}{9x}$ and state the excluded value.

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

3. Simplify $\frac{x^2+5x+6}{x^2+4x+3}$.

Answer: $\frac{x+2}{x+1}$, $x\neq-1,-3$

4. Simplify $\frac{x^2-25}{x^2-10x+25}$.

Answer: $\frac{x+5}{x-5}$, $x\neq5$

5. Simplify $\frac{x^2+7x+12}{x^2+5x+6}$.

Answer: $\frac{x+4}{x+2}$, $x\neq-2,-3$

6. Simplify $\frac{x^2-4x}{x^2-16}$.

Answer: $\frac{x}{x+4}$, $x\neq4,-4$

7. Simplify $\frac{15x}{25x^2}$.

Answer: $\frac{3}{5x}$, $x\neq0$

8. Simplify $\frac{x^2+2x+1}{x+1}$.

Answer: $x+1$, $x\neq-1$

9. Simplify $\frac{4x^2-9}{2x+3}$.

Answer: $2x-3$, $x\neq-\frac{3}{2}$

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

Answer: $\frac{x-1}{x+1}$, $x\neq-1$