If $\dfrac{x}{(x-2)(x+3)}=\dfrac{A}{x-2}+\dfrac{B}{x+3}$, find $A$.

If (x)/((x-2)(x+3))=(A)/(x-2)+(B)/(x+3), find A.

Question 4 of 8

\dfrac{x}{(x-2)(x+3)}=\dfrac{A}{x-2}+\dfrac{B}{x+3}

Yanam BieapSubjective· 2mImportance★★★★★est

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Multiply both sides by $(x-2)(x+3)$ , then plug in $x=2$ so the $B$ term drops out, leaving $A$ alone.

$x=A(x+3)+B(x-2)$

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