Question

Resolve into partial fractions:
$\frac{46+13x}{12x^2-11x-15}$

Answer 1

The table give general form of the partial fractions :

So , $\frac{46+13x}{12x^2-11x-15}=\frac{46+13x}{(3x-5)(4x+3)}$

$=>\frac{46+13x}{(3x-5)(4x+3)}=\frac{A}{3x-5}+\frac{B}{4x+3}$

$=>46+13x=A(4x+3)+B(3x-5)$

For $x=-\frac{3}{4}=>46-\frac{13}{4}=B(-\frac{9}{4}-5)$

$=>\frac{145}{4}=B(-\frac{29}{4})$

$=>B=-5$

For $x=\frac{5}{3}=>46+\frac{5}{3}=A(\frac{20}{3}+3)$

$=>\frac{203}{3}=A\left(\frac{29}{3}\right)$

$=>A=7$

Therefore , $\frac{46+13x}{12x^2-11x-15}=\frac{7}{3x-5}-\frac{5}{4x+3}$