Additional Mathematics – Equations, inequalities and graphs | e-Consult
Equations, inequalities and graphs (1 questions)
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First note that \(t\neq1\) (denominator restriction).
Multiply both sides by \(t-1\):
\(t^{2}-4t+3 = (t+2)(t-1)\).
Expand the right‑hand side:
\(t^{2}-4t+3 = t^{2}+2t - t -2 = t^{2}+t-2\).
Subtract \(t^{2}+t-2\) from both sides:
\(-4t+3 - (t-2) = 0\) → \(-4t+3 -t +2 =0\) → \(-5t+5=0\).
Thus \(-5t+5=0\) gives \(t=1\).
However, \(t=1\) is excluded because it makes the original denominator zero. Therefore there is no valid solution.
Conclusion: the equation has no solution in the real numbers.