Can u help me with this Subtracting Algebraic Expressions 50pts
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Can u help me with this Subtracting Algebraic Expressions 50pts
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SUBTRACTING ALGEBRAIC EXPRESSIONS
[tex] \frac{5}{ {x}^{2} - 4} - \frac{2}{x + 2} [/tex]
Since, the expressions don't have common denominators, let's first find the LCD by factoring
[tex] \: \: \: \: \: \: \: \: \: \: \frac{5}{ {x}^{2} - 4 } \: \: \: \: \: \: \: \: \: - \: \: \: \: \frac{2}{x + 2} \\ (x + 2)(x - 2) \: \: \: \: \: \: (x + 2)[/tex]
[tex]Now \: the \: LCD \: is : \\ ( x+2) (x-2) = {x}^{2} - 4[/tex]
Then change each rational expression into an equivalent expression with that LCD then solve.
[tex] \frac{5}{ (x + 2)(x - 2) } - \frac{2}{x + 2} \times \frac{(x - 2)}{(x - 2)} \\ = \frac{(5) - (2x - 4)}{(x + 2)(x - 2)} \\ = \frac{5 - 2x + 4}{(x + 2)(x - 2)} \\ = \frac{ - 2x + 9}{(x + 2)(x - 2)} [/tex]
[tex] Now \: the\: answer\: is\: \frac{ - 2x + 9}{(x + 2)(x - 2)} [/tex]
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