+0  
 
+1
125
3
avatar

There are values A and B such that \(\frac{Bx-11}{x^2-7x+10}=\frac{A}{x-2}+\frac{3}{x-5}.\)
Find A+B.

 May 9, 2021
 #1
avatar
-1

By partial fractions, A = 1 and B = 3.

 May 9, 2021
 #2
avatar+32567 
+4

As follows;

 

 May 9, 2021
 #3
avatar+26213 
+2

There are values A and B such that
\(\dfrac{Bx-11}{x^2-7x+10}=\dfrac{A}{x-2}+\dfrac{3}{x-5}\)
Find A+B.

 

\(\small{ \begin{array}{|lrcll|} \hline & \dfrac{Bx-11}{x^2-7x+10} &=&\dfrac{A}{x-2}+\dfrac{3}{x-5} \quad | \quad x^2-7x+10 =(x-2)(x-5) \\\\ & \dfrac{Bx-11}{(x-2)(x-5)} &=&\dfrac{A}{x-2}+\dfrac{3}{x-5} \quad | \quad * (x-2)(x-5)\\\\ & Bx-11 &=& A(x-5)+ 3(x-2) \\ & \mathbf{ Bx-A(x-5) } &=& \mathbf{ 3(x-2) + 11 } \\ \hline 1.~ x=0:& 0 +5A &=& -6+11 \\ & 5A &=& 5 \\ & \mathbf{A} &=& \mathbf{1} \\ \hline 2.~ x =5:& 5B - 0 &=& 9+11 \\ & 5B &=& 20 \\ & \mathbf{B} &=& \mathbf{4} \\ \hline \end{array} }\)


\(\mathbf{A+B = 5}\)

 

laugh

 May 9, 2021
edited by heureka  May 9, 2021
edited by heureka  May 9, 2021

22 Online Users

avatar