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Sagot :

[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]

  • Simplify ⇨ 1/x(x+a) + 1/x(x-a)

[tex] \large \boxed{\mathbb{ANSWER \: WITH \: EXPLANATION} \downarrow}[/tex]

[tex] \sf\frac { 1 } { x ( x + a ) } + \frac { 1 } { x ( x - a ) } \\ [/tex]

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of [tex]x\left(x+a\right)[/tex] and [tex]x\left(x-a\right)[/tex] is [tex]x\left(x+a\right)\left(x-a\right)[/tex]. Multiply [tex]\frac{1}{x\left(x+a\right)} times \frac{x-a}{x-a}[/tex]. Multiply [tex]\frac{1}{x\left(x-a\right)} times \frac{x+a}{x+a}[/tex].

[tex] \sf\frac{x-a}{x\left(x+a\right)\left(x-a\right)}+\frac{x+a}{x\left(x+a\right)\left(x-a\right)} \\ [/tex]

Because [tex]\frac{x-a}{x\left(x+a\right)\left(x-a\right)}[/tex] and [tex]\frac{x+a}{x\left(x+a\right)\left(x-a\right)}[/tex] have the same denominator, add them by adding their numerators.

[tex] \sf\frac{x-a+x+a}{x\left(x+a\right)\left(x-a\right)} \\ [/tex]

Combine like terms in x-a+x+a.

[tex] \sf\frac{2x}{x\left(x+a\right)\left(x-a\right)} \\ [/tex]

Cancel out x in both the numerator and denominator.

[tex] \sf\frac{2}{\left(x+a\right)\left(x-a\right)} \\ [/tex]

Expand [tex]\left(x+a\right)\left(x-a\right)[/tex].

[tex] \boxed{\boxed{ \bf\frac{2}{x^{2}-a^{2}}}} \\ [/tex]