Given 2/x^2 5/x+2 =0Since, LCM of x^2 and x is x^2 (2 5x + 2x^2)/x^2 = 0⇒ 2x^2 5x + 2 = 0⇒ 2x^2 4x x +2 = 0⇒ 2x(x 2) 1(x 2) = 0∴ (x 2)(2x 1) = 0 ...

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Addition of Rational Expressions

2/x2-5/x+2=0

Question

Write in factorised form: $\frac{2}{x^{2}} - \frac{5}{x} + 2 = 0$

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Solution

Given $\frac{2}{x^{2}} - \frac{5}{x} + 2 = 0$
Since, LCM of $x^{2}$ and $x$ is $x^{2}$
$\frac{(2 - 5 x + 2 x^{2})}{x^{2}} = 0$
$\Rightarrow 2 x^{2} - 5 x + 2 = 0$
$\Rightarrow 2 x^{2} - 4 x - x + 2 = 0$
$\Rightarrow 2 x (x - 2) - 1 (x - 2) = 0$
$∴ (x - 2) (2 x - 1) = 0$

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