Conditions present after solving for xThe question asked me to solve x 2 + 2 x − 8 x 2 − x − 2 = 3The answer is x = 0.5, which I worked out, but in the answers it says that I must state the condition that x ≠ 2 to get full marks. Why is this condition present? How can I recognise when a condition exists, when I encounter similar problems?

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Conditions present after solving for xThe question asked me to solve                              x          2                +        2        x        −        8                              x          2                −        x        −        2              =  3The answer is   x  =  0.5, which I worked out, but in the answers it says that I must state the condition that   x  ≠  2 to get full marks. Why is this condition present? How can I recognise when a condition exists, when I encounter similar problems?

Ashly Kaufman · Accepted Answer

When solving this equation you assume that       x    2    −  x  −  2  ≠      0      ⟹        x  ≠      −  1  ,  2. In general while solving an equation make sure that the denominator is not equal   0.

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