Question 1043309
{{{1/(x(x+1))=a/x-b/(x+1)}}}


{{{(1/(x(x+1)))(x(x+1))=(a/x-b/(x+1))(x(x+1))}}}


{{{1=a(x+1)-bx}}}


{{{1=ax+a-bx}}}


Arrange into expressions of x.


{{{ax-bx+a=1}}}


{{{(a-b)x+a=1}}}


Be reminded, EXPRESSIONS of x...


{{{(a-b)x+a=0*x+1}}}
Compare the corresponding parts to build a simple system of equations.
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{{{system(a-b=0,a=1)}}}



Not yet solved for both a and b, but you can now see how to finish.