Maths-
General
Easy

Question

If x ≠ -1, what is the value of open parentheses fraction numerator 1 over denominator straight x space plus space 1 end fraction close parentheses space open parentheses 2 space plus space 2 straight x close parentheses ?

  1. 2

The correct answer is: 2


    HINT: Solve using distributive property.
    Complete step by step solution:
    We are given open parentheses fraction numerator 1 over denominator straight x space plus space 1 end fraction close parentheses space left parenthesis 2 space plus space 2 straight x right parenthesis
    Distributive property states that a(b + c) = ab + ac
    By applying this property, we get fraction numerator 2 space plus space 2 straight x over denominator 1 space plus space straight x end fraction
    On taking the common factor 2 from the numerator, we get fraction numerator 2 left parenthesis 1 space plus space x right parenthesis over denominator left parenthesis x space plus space 1 right parenthesis end fraction.
    This can be rewritten as fraction numerator 2 left parenthesis straight x space plus space 1 right parenthesis over denominator left parenthesis straight x space plus space 1 right parenthesis end fraction (Using commutative property, we have (x + 1) = (1 + x))
    On cancelling (x + 1) from both numerator and denominator, we get the value as 2.

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