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Algebra

Question 9 of 9

Factorising Quadratic Equations

Question

Factorise \(\dfrac{3}{2b} - \dfrac{13}{2(b+2)} = 6\)

Show solution Hide solution Fully worked — 6 steps
  1. Multiply both sides by \(2b(b + 2)\)
    \[ \frac{3}{2b} - \frac{13}{2(b+2)} = 6 \]
    \[ 3(b + 2) - 13b = 12b(b + 2) \]
  2. Multiply \(3\) and \((b + 2)\); \(12b\) and \((b + 2)\)
    \[ 3b + 6 - 13b = 12b^2 + 24b \]
  3. Combine similar terms and rearrange in the form \(ax^2 + bx + c = 0\)
    \[ 12b^2 + 34b - 6 = 0 \]
  4. Factorise
    \[ (6b - 1)(2b + 6) = 0 \]
  5. Using the zero-factor theorem, equate each factor to 0

    Then either

    \[ 6b - 1 = 0 \Rightarrow b = \frac{1}{6} \]

    or

    \[ 2b + 6 = 0 \Rightarrow b = -3 \]
  6. State the solutions

    The solutions are \(b = \frac{1}{6}\) or \(b = -3\). That is, \(b\) is one sixth and \(b\) is minus three.