Question
If $$x + \frac{1}{{x + 1}} = 1,$$ then $${\left( {x + 1} \right)^5}$$ + $$\frac{1}{{{{\left( {x + 1} \right)}^5}}}$$ equals?
Answer: Option B
$$\eqalign{
& x + \frac{1}{{x + 1}} = 1 \cr
& {\text{Adding both 1 sides}} \cr
& \Rightarrow x + 1 + \frac{1}{{x + 1}} = 1 + 1 \cr
& \Rightarrow \left( {x + 1} \right) + \frac{1}{{\left( {x + 1} \right)}} = 2 \cr
& {\text{Put }}x + 1 = 1 \cr
& {\text{And }}\frac{1}{{x + 1}} = 1 \cr
& \therefore {\left( {x + 1} \right)^5}{\text{ + }}\frac{1}{{{{\left( {x + 1} \right)}^5}}} \cr
& = 1 + 1 \cr
& = 2 \cr} $$
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$$\eqalign{
& x + \frac{1}{{x + 1}} = 1 \cr
& {\text{Adding both 1 sides}} \cr
& \Rightarrow x + 1 + \frac{1}{{x + 1}} = 1 + 1 \cr
& \Rightarrow \left( {x + 1} \right) + \frac{1}{{\left( {x + 1} \right)}} = 2 \cr
& {\text{Put }}x + 1 = 1 \cr
& {\text{And }}\frac{1}{{x + 1}} = 1 \cr
& \therefore {\left( {x + 1} \right)^5}{\text{ + }}\frac{1}{{{{\left( {x + 1} \right)}^5}}} \cr
& = 1 + 1 \cr
& = 2 \cr} $$
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