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Reducing Equations to Simpler Form

Solve: x - ...

Question

Solve: $\frac{x - 2}{x - 4} = \frac{x + 4}{x - 2}$

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Solution

Given $\frac{x - 2}{x - 4} = \frac{x + 4}{x - 2}$

$⟹ (x - 2)^{2} = (x - 4) (x + 4)$

$⟹ x^{2} - 4 x + 4 = x^{2} - 16$

$⟹ 4 x = 20$

$⟹ x = \frac{20}{4} = 5$

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Similar questions

| x^{2} + x - 4 | = | x^{2} - 4 | + | x |

x :

\frac{1}{x + 1} + \frac{2}{x + 2} = \frac{4}{x + 4}, x \neq - 1, - 2, - 4

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\frac{1}{x + 2} + \frac{2}{x + 2} = \frac{4}{x + 4}

Q. Solve for x:

\frac{1}{x + 1} + \frac{2}{x + 2} = \frac{4}{x + 4}, x \neq - 1, - 2, - 4

\frac{x - 2}{x + 2} + \frac{x + 2}{x - 2} = 4

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Reducing Equations to Simpler Form

Standard VIII Mathematics

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