Question

resolve into palatial fraction x-1/(x+1)(x-2)​

Answer 1

$\bigstar$ Answer :

$\frac{x-1}{(x+1)(x-2)}=\frac{\frac{2}{3} }{x+1}+\frac{\frac{1}{3} }{x-2}$

$\bigstar$ Step-by-step explanation :

$\star$ Let

$\frac{x-1}{(x+1)(x-2)}=\frac{A}{x+1}+\frac{B}{x-2}\\\\=>\frac{x-1}{(x+1)(x-2)}=\frac{A(x-2+B(x+1))}{(x+1)(x-2)} \\\\=>x-1=Ax-2A+Bx+B\\\\=>x-1=(A+B)x-(2A-B)\\\\=>1=A+B , 1=2A-B\\\\=>1=A+B , B = 2A-1...(1)\\\\=>1=A+2A-1\\\\=>3A=2\\\\=>A=\frac{2}{3}$

Now . sub. A=2/3 in (1) , we get,

$B=2*\frac{2}{3} -1\\\\=>B=\frac{4}{3}-1\\\\ =>B=\frac{1}{3}$

$\bigstar$  $\frac{x-1}{(x+1)(x-2)}=\frac{\frac{2}{3} }{x+1}+\frac{\frac{1}{3} }{x-2}$

$\star$ More Information :

$\star$ Partial Fractions..

• Start with a Proper Rational Expressions (if not, do division first)
• Factor the bottom into: linear factors. ...
• Write out a partial fraction for each factor (and every exponent of each)
• Multiply the whole equation by the bottom.
• Solve for the coefficients by. substituting zeros of the bottom. ...

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