Express f(x) =3\x²- 1 in partial fraction
1 answer:
3/(<em>x</em> ² - 1) = 3/((<em>x</em> - 1) (<em>x</em> + 1)) = <em>a</em>/(<em>x</em> - 1) + <em>b</em>/(<em>x</em> + 1)
==> 3 = <em>a</em> (<em>x</em> + 1) + <em>b</em> (<em>x</em> - 1)
==> 3 = (<em>a</em> + <em>b</em>) <em>x</em> + <em>a</em> - <em>b</em>
==> <em>a</em> + <em>b</em> = 3 and <em>a</em> - <em>b</em> = 0
==> <em>a</em> = <em>b</em>
==> <em>a</em> + <em>b</em> = 2<em>a</em> = 3 ==> <em>a</em> = 2/3 and <em>b</em> = 2/3
So you have
3/(<em>x</em> ² - 1) = 2/(3(<em>x</em> - 1)) + 2/(3(<em>x</em> + 1))
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