Mathematics 10 — Exercise 2.1 · Q1 (vi)

Full question

Write the following quadratic equation in standard form: (6 × x+6)/(20-x) = 1/x. where x ≠ 0, 20.

Step-by-step solution

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

   $$x^2-20\times x\ne 0$$

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

   $$\left(\frac{6\times x+6}{20-x}\right)\times \left(x^2-20\times x\right)=\frac{x^2-20\times x}{x}$$

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

   $$6\times x^2+7\times x-20=0$$

Answer

The final answer is shown below.