Mathematics 10 — Exercise 4.1 · Q2 (iii)

Full question

For the following functions, find f/g.

Step-by-step solution

1. A denominator cannot be zero. Solve its zero equation to exclude those inputs.

   $$2\times x+4\ne 0$$

2. Write the numerator function above the denominator function.

   $$\frac{x+2}{2\times x+4}$$

3. Factor the numerator.

   $$x+2$$

4. Factor the denominator.

   $$2\times \left(x+2\right)$$

5. Cancel only common factors, keeping all original excluded inputs.

   $$\frac{x+2}{2\times \left(x+2\right)}$$

6. Write the simplified quotient with those domain restrictions.

   $$\frac{1}{2}$$

Answer

The final answer is shown below.