Solve equation, given below, using factorisation method:

$(1 + \frac{1}{x + 1}) (1 - \frac{1}{x - 1}) = \frac{7}{8}$

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Solution

$open parentheses 1 plus fraction numerator 1 over denominator x plus 1 end fraction close parentheses open parentheses 1 minus fraction numerator 1 over denominator x minus 1 end fraction close parentheses equals 7 over 8 open parentheses fraction numerator x plus 1 plus 1 over denominator x plus 1 end fraction close parentheses open parentheses fraction numerator x minus 1 minus 1 over denominator x minus 1 end fraction close parentheses equals 7 over 8 open parentheses fraction numerator x plus 2 over denominator x plus 1 end fraction close parentheses open parentheses fraction numerator x minus 2 over denominator x minus 1 end fraction close parentheses equals 7 over 8 fraction numerator x squared minus 4 over denominator x to the power of 2 space end exponent minus 1 end fraction equals 7 over 8 8 x to the power of 2 space end exponent minus 32 equals 7 x to the power of 2 space end exponent minus 7 x to the power of 2 space end exponent equals 25 x equals plus-or-minus 5$

Using factorization method:

We are getting the equation, $x^{2} = 25 \Rightarrow x^{2} - 25 = 0 \Rightarrow x^{2} - 5^{2} = 0 \Rightarrow (x + 5) (x - 5) = 0 \Rightarrow x = 5 o r x = - 5$

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