[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13}{a + 5} + \cfrac{24}{a + 4} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13(a + 4) + 24(a + 5)}{(a + 5)(a + 4)} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13a + 52+ 24a + 120}{a {}^{2} + 5a + 4a + 20} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ 37a + 172}{a {}^{2} +9a + 20} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: 3( {a }^{2} + 9a + 20) = 37a + 172[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} + 27a + 60 = 37a + 172[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} + 27a - 37a + 60 - 172 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} - 10a - 112= 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} - 24a + 14a - 112 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3a(a - 8) + 14(a - 8) = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: (a - 8) + (3a + 14) = 0[/tex]
So, required values of " a " are :
[tex]\qquad \sf \dashrightarrow \: a = 8 \: \: \: or \: \: \: a = - \cfrac{ 14}{3} [/tex]
