How do you solve $\frac{x - 3}{x} = \frac{x - 3}{x - 6}$ $(x - 3) /x = (x - 3) / (x - 6)$ ?

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How do you solve $\frac{x - 3}{x} = \frac{x - 3}{x - 6}$ $(x - 3) /x = (x - 3) / (x - 6)$ ?

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Answer 1 · 2017-02-18T03:40:27

$x = 3$ $x = 3$

Explanation:

Put the equation in $y = 0$ $y=0$ form:

$y = \frac{x - 3}{x} = \frac{x - 3}{x - 6}$ $y = (x-3)/x = (x-3)/(x-6)$

$y = \frac{x - 3}{x} - \frac{x - 3}{x - 6} = 0$ $y = (x-3)/x - (x-3)/(x-6) = 0$

Find a common denominator:
$y = \frac{x - 3}{x} \cdot \frac{x - 6}{x - 6} - \frac{x - 3}{x - 6} \cdot \frac{x}{x} = 0$ $y = (x-3)/x * (x-6)/(x-6) - (x-3)/(x-6) * x/x= 0$

Combine under the same denominator:

$y = \frac{(x - 3) (x - 6) - x (x - 3)}{x (x - 6)} = 0$ $y = ((x-3)(x-6) - x(x-3))/(x(x-6)) = 0$

Factor the numerator: $(x - 3) (x - 6 - x) = - 6 (x - 3)$ $(x-3)(x-6-x) = -6(x-3)$

$y = \frac{- 6 (x - 3)}{x (x - 6)} = 0$ $y = (-6(x-3))/(x(x-6)) = 0$

The numerator gives a a solution when $y = 0$ $y = 0$ , when $x = 3$ $x = 3$

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How do you solve $\frac{x - 3}{x} = \frac{x - 3}{x - 6}$ $(x - 3) /x = (x - 3) / (x - 6)$ ?

1 Answer

Explanation:

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How do you solve $\frac{x - 3}{x} = \frac{x - 3}{x - 6}$ $(x - 3) /x = (x - 3) / (x - 6)$ ?