Mathematics 10 — Exercise 2.1 · Q1 (v)

Full question

Write the following quadratic equation in standard form: 2 × x+1/x = 5-1/x. where x ≠ 0.

Step-by-step solution

1. A denominator cannot equal zero. Keep the original excluded values throughout the calculation.

   $$x\ne 0$$

2. Multiply BOTH sides by the common denominator to remove the fractions.

   $$x\times \left(2\times x+\frac{1}{x}\right)=x\times \left(5-\frac{1}{x}\right)$$

3. Expand the brackets and subtract the right-hand terms from both sides. Collect powers of the variable.

   $$2\times x^2-5\times x+2=0$$

Answer

The final answer is shown below.