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Question

Which of the following is equivalent to fraction numerator 4 x squared plus 6 x over denominator 4 x plus 2 end fraction  ?

  1. x
  2. x + 4
  3. x minus fraction numerator 2 over denominator 4 x plus 2 end fraction
  4. x plus 1 minus fraction numerator 2 over denominator 4 x plus 2 end fraction

hintHint:

Hint:
  • An expression is a combination of symbols used in algebra, containing one or more numbers, variables, and arithmetic operations

The correct answer is: x minus fraction numerator 2 over denominator 4 x plus 2 end fraction


    Explanation:
    • We have given an expression fraction numerator 4 x squared plus 6 x over denominator 4 x plus 2 end fraction
    • We have to simplify the given expression .
    • We will try to factorize the numerator part by adding and subtracting some numbers. After that, we will split the fraction into two parts.
    Step 1 of 2:
    We have given expressionfraction numerator 4 x squared plus 6 x over denominator 4 x plus 2 end fraction
    Now add and subtract from the numerator and the factorize it
    So,
    fraction numerator 4 x squared plus 6 x plus 2 minus 2 over denominator 4 x plus 2 end fraction
    Now, On factorization we get
    fraction numerator left parenthesis x plus 1 right parenthesis left parenthesis 4 x plus 2 right parenthesis minus 2 over denominator 4 x plus 2 end fraction
    Then, Rewrite the above expression
    fraction numerator left parenthesis x plus 1 right parenthesis left parenthesis 4 x plus 2 right parenthesis over denominator 4 x plus 2 end fraction minus fraction numerator 2 over denominator 4 x plus 2 end fraction
    not stretchy rightwards double arrow x plus 1 minus fraction numerator 2 over denominator 4 x plus 2 end fraction
    So, Option (c) is correct.
    Final answer:
    Hence, The expression fraction numerator 4 x squared plus 6 x over denominator 4 x plus 2 end fraction is equivalent to x plus 1 minus fraction numerator 2 over denominator 4 x plus 2 end fraction.
    le, Option (c) is correct.

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