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Particular Solution of a Differential Equation

Simplify: 1...

Question

Simplify: $\frac{1}{x^{2} - 5 x + 6} - \frac{1}{x^{2} - 3 x + 2}$

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Solution

Given,

$\frac{1}{x^{2} - 5 x + 6} - \frac{1}{x^{2} - 3 x + 2}$

$= \frac{1}{(x - 2) (x - 3)} - \frac{1}{(x - 1) (x - 2)}$

$= \frac{x - 1}{(x - 2) (x - 3) (x - 1)} - \frac{x - 3}{(x - 2) (x - 3) (x - 1)}$

$= \frac{x - 1 - (x - 3)}{(x - 2) (x - 3) (x - 1)}$

$= \frac{2}{(x - 2) (x - 3) (x - 1)}$

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Similar questions

\frac{1}{x^{2} + 3 x + 2} + \frac{1}{x^{2} + 5 x + 6} - \frac{2}{x^{2} + 4 x + 3}

Q. Simplify the following polynomials in the simplest form:

\frac{1}{x^{2} + 3 x + 2} + \frac{1}{x^{2} + 5 x + 6} - \frac{2}{x^{2} + 4 x + 3}

Q. The expression

\frac{x^{2} - 3 x + 2}{x^{2} - 5 x + 6} \div \frac{x^{2} - 5 x + 4}{x^{2} - 7 x + 12}

, when simplified, is

\sqrt{\frac{(x^{2} + 3 x + 2) (x^{2} + 5 x + 6)}{x^{2} (x^{2} + 4 x + 3)}}

\frac{x^{2} - 3 x + 2}{x^{2} - 1} =

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