Express in partial fractions frac 11 2 6x 2 - x... - JAMB Mathematics 1998 Question
Express in partial fractions \(\frac{11 + 2}{6x^2 - x - 1}\)
A
\(\frac{1}{3x - 1}\) + \(\frac{3}{2x + 1}\)
B
\(\frac{3}{3x + 1}\) - \(\frac{1}{2x - 1}\)
C
\(\frac{3}{3x + 1}\) - \(\frac{1}{2x - 1}\)
D
\(\frac{1}{3x + 1}\) + \(\frac{3}{2x - 1}\)
correct option: d
\(\frac{11 + 2}{6x^2 - x - 1}\) = \(\frac{11 + 2}{3x + 1}\)
= \(\frac{A}{3x + 1}\) + \(\frac{B}{2x - 1}\)
11x = 2 = A(2x - 1) + B(3x + 1)
put x = \(\frac{1}{2}\)
= -\(\frac{-5}{3}\)
= -\(\frac{-5}{3}\)A \(\to\) A = 1
∴ \(\frac{11x +2}{6x^2 - x - 1}\) = \(\frac{1}{3x + 1}\) + \(\frac{3}{2x - 1}\)
= \(\frac{A}{3x + 1}\) + \(\frac{B}{2x - 1}\)
11x = 2 = A(2x - 1) + B(3x + 1)
put x = \(\frac{1}{2}\)
= -\(\frac{-5}{3}\)
= -\(\frac{-5}{3}\)A \(\to\) A = 1
∴ \(\frac{11x +2}{6x^2 - x - 1}\) = \(\frac{1}{3x + 1}\) + \(\frac{3}{2x - 1}\)
Please share this, thanks:
Add your answer
No responses