Maths-
General
Easy

Question

Describe the error student made in multiplying and simplifyingfraction numerator x plus 2 over denominator x minus 2 end fraction cross times fraction numerator x squared minus 4 over denominator x squared plus x minus 2 end fraction

hintHint:

The expansions of certain identities are:
open parentheses straight x squared minus straight a squared close parentheses equals left parenthesis straight x minus straight a right parenthesis left parenthesis straight x plus straight a right parenthesis
straight x squared plus left parenthesis straight a plus straight b right parenthesis straight x plus ab equals left parenthesis straight x plus straight a right parenthesis left parenthesis straight x plus straight b right parenthesis
We are asked to describe the error made by the student and simplify the expression.

The correct answer is: The error made by the student is that he/she cut out the value x from the term which is not possible


    Step 1 of 2:
    The given expression isfraction numerator straight x plus 2 over denominator straight x minus 2 end fraction cross times fraction numerator straight x squared minus 4 over denominator straight x squared plus straight x minus 2 end fraction
    Simplify the expression using identities,
    fraction numerator straight x plus 2 over denominator straight x minus 2 end fraction cross times fraction numerator straight x squared minus 4 over denominator straight x squared plus straight x minus 2 end fraction equals fraction numerator straight x plus 2 over denominator straight x minus 2 end fraction cross times fraction numerator straight x squared minus 2 squared over denominator straight x squared plus 2 straight x minus straight x minus 2 end fraction
    equals fraction numerator straight x plus 2 over denominator straight x minus 2 end fraction cross times fraction numerator left parenthesis straight x plus 2 right parenthesis left parenthesis straight x minus 2 right parenthesis over denominator straight x left parenthesis straight x plus 2 right parenthesis minus 1 left parenthesis straight x plus 2 right parenthesis end fraction
    equals fraction numerator straight x plus 2 over denominator straight x minus 2 end fraction cross times fraction numerator left parenthesis straight x plus 2 right parenthesis left parenthesis straight x minus 2 right parenthesis over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x plus 2 right parenthesis end fraction
    equals fraction numerator straight x plus 2 over denominator straight x minus 1 end fraction
    Step 2 of 2:
    The error made by the student is that he/she cut out the value x from the term which is not possible. To cut off, the values has to be common for every single term in the expression which is not the case here.

    To cut off a value from an expression, the value should be common for each and every term in the expression.

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