Partial Fractions in Algebra, Exercises of Mathematics

Download Partial Fractions in Algebra and more Exercises Mathematics in PDF only on Docsity! Algebra Partial fractions 1. Solution: = + 2 = A ( x + 4) + Bx Put x = 0, 2 = 4A  A = Put x =  4 2 = 4B  B =   The partial fractions are  2. Solution: = = + Put x = 1  1 = A (2)  A = Put x = 1 1 = B ( 2 )  B =  The partial fractions are  3. Solution: = =  x = A (x + 2) + B ( x+ 1) Put x = 1 1 = A (1)  A = 1 Put x = 2 2 = B(1)  B = 2  The partial fraction are =  2 x ( x+4) 1 1 2x 2(x + 4) 1 2 2 A B x ( x + 4) x x + 4 1 2 x x A B x 2 – 1 (x +1)(x –1) x +1 x –1 1 1 2( x+ 1) 2(x 1) 1 2 1 2 x x 2 – 1 x (x + 1)( x + 2)  x A B ( x + 1)( x +2 ) x + 1 x + 2 1 2 x + 1 x + 2 4. Solution: = + x + 1 = A (x – 1) + Bx put x = 0 1 = A ( 1)  A = 1 put x = 1 2 = B (1)  B = 2  The partial fraction are =  5   Solution: = + 2x  3 = A( x + 3) + B(x +2) put x =  2, 7 = A(1)  A = 7 put x =  3, 9 = B(1)  B = –9   The partial fraction are =  6. x x A B x 2 + 2x+ 1 (x +1) 2 (x+1) (x+1) 2 x = A (x+1) + B Put x = 1 1 = B Put x = 0, 0 = A + B  A = 1  The partial fractions are  x + 1 x( x  1) A B x x – 1 1 2 x x – 2 x + 1 x( x - 1) 2x  3 ( x + 2)( x + 3) 2x 3 (x + 2)( x + 3) A B x + 2 x + 3 7 9 x+ 2 x +3 Solution: Let = = + 1 1 x + 1 ( x +1) 2 x x 2 + 2x+ 1