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If((x + 1 ))/((2x - 1 ) (3x + 1 ))= (A)/((2x - 1 ))+ (B)/((3x+ 1)) , then16 A +9 Bisequalto

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Solution : ` ((X + 1 ))/((2x - 1 )(3x+ 1 )) = (A)/((2x - 1)) + (B)/((3x+ 1 )) `
` rArrx + 1= A (3x + 1 ) + B(2x - 1) `
` rArrx + 1=x (3A + 2B)+(A -B) `
`3A +2B = 1`
` A -B = 1`
` rArrA =1 + B `
` 3( 1 + B)+2B =1`
`rArr3+5B = 1`
` B = (-2)/(5) `
` A =1+B =1-( 2 ) /(5) `
` A =(3)/(5) `
`therefore16 A +9B =16 ((3)/(5)) +9 ((-2)/(5)) =(30)/(5)= 6 `


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