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Algebra 1SuperchallengeRational Expressions

Rational Expressions · Superchallenge problem

Find the sum of all real solutions of 1x(x+1)+1(x+1)(x+2)+1(x+2)(x+3)+⋯+1(x+9)(x+10)=512\dfrac{1}{x(x+1)} + \dfrac{1}{(x+1)(x+2)} + \dfrac{1}{(x+2)(x+3)} + \cdots + \dfrac{1}{(x+9)(x+10)} = \dfrac{5}{12} (ten fractions in all).