begin{array}{l}text { fineakb } frac{4 x+5}{(x-5)(x+3)}=frac{A}{x-5}+frac{B}{x+2}end{array}

Question

begin{array}{l}text { fineakb }  frac{4 x+5}{(x-5)(x+3)}=frac{A}{x-5}+frac{B}{x+2}end{array}

Accepted Answer

Step:1 ：Given the equation: (frac{4x+5}{(x-5)(x+3)} = frac{A}{x-5} + frac{B}{x+3})Step:2 ：Clear the denominators by multiplying both sides by ((x-5)(x+3)): (4x+5 = A(x+3) + B(x-5))Step:3 ：Solve for A and B:Step:4 ：Final Answer: (A = boxed{frac{25}{8}}) and (B = boxed{frac{7}{8}})

Answer

Step: 1 ：Given the equation: (frac{4x+5}{(x-5)(x+3)} = frac{A}{x-5} + frac{B}{x+3})Step: 2 ：Clear the denominators by multiplying both sides by ((x-5)(x+3)): (4x+5 = A(x+3) + B(x-5))Step: 3 ：Solve for A and B:Step: 4 ：Final Answer: (A = boxed{frac{25}{8}}) and (B = boxed{frac{7}{8}})

$\begin{array}{l}\text { fineakb } \\ \frac{4 x+5}{(x-5)(x+3)}=\frac{A}{x-5}+\frac{B}{x+2}\end{array}$

Answer

Popular Problems