Question 12

The number of real values of $$x$$ satisfying the equation $$\frac{3x^2 - 21x}{x^2 - 7x} = x - 4$$ is

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For $$x \neq 0$$ and $$x \neq 7$$ the left side simplifies as $$\frac{3x(x - 7)}{x(x - 7)} = 3$$, so the equation becomes $$3 = x - 4$$, giving $$x = 7$$. But $$x = 7$$ makes the original denominator zero, so it is not admissible. Hence there is no real solution.

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