Mathematics 10 — Exercise 4.1 · Q2 (iv)

Full question

For the following functions, find g/f.

Step-by-step solution

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

   $$x+2\ne 0$$

2. Write the numerator function above the denominator function.

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

3. Factor the numerator.

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

4. Factor the denominator.

   $$x+2$$

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

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

6. Write the simplified quotient with those domain restrictions.

   $$2$$

Answer

The final answer is shown below.