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What two rational expression sum to 3x-2/x^2-x-12

 
 Jan 24, 2023
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Hi Lina,

Welcome to Web2.0calc forum  wink

 

This is called partial fractions, it comes in useful when doing calculus.

 

\(\frac{3x+2}{x^2-x-12}=\frac{A}{(x-4)}+\frac{B}{(x+3)}\\ So\\ Ax+3A+Bx-4B=3x+2\\ (A+B)x+(3A-4B)=3x+2\\ A+B=3\qquad and \qquad 3A-4B=2\\ A=3-B\\ \text{sub to get B}\\ 3(3-B)-4B=2\\ -7B+9=2\\ B=1\\ A=3-1=2\\ \frac{3x+2}{x^2-x-12}=\frac{2}{(x-4)}+\frac{1}{(x+3)}\\ \)

 

You can finish :)

 
 Jan 24, 2023

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