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Question

𝑉𝑒𝑟𝑖𝑓𝑦 open parentheses fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator 2 over denominator negative 5 end fraction close parentheses plus fraction numerator negative 13 over denominator 22 end fraction equals fraction numerator negative 7 over denominator 11 end fraction plus open parentheses fraction numerator 2 over denominator negative 5 end fraction plus fraction numerator negative 13 over denominator 22 end fraction close parentheses

hintHint:

Solve the LHS part and RHS part separately and then compare.

The correct answer is: verified.


    To verify open parentheses fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator 2 over denominator negative 5 end fraction close parentheses plus fraction numerator negative 13 over denominator 22 end fraction equals fraction numerator negative 7 over denominator 11 end fraction plus open parentheses fraction numerator 2 over denominator negative 5 end fraction plus fraction numerator negative 13 over denominator 22 end fraction close parentheses
    Express the rational numbers with positive denominator by multiplying with -1.

    Here, fraction numerator 2 over denominator negative 5 end fraction equals fraction numerator 2 cross times negative 1 over denominator negative 5 cross times negative 1 end fraction equals fraction numerator negative 2 over denominator 5 end fraction
    Consider the LHS part, we have open parentheses fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator negative 2 over denominator 5 end fraction close parentheses plus fraction numerator negative 13 over denominator 22 end fraction…(i)
    Determine the LCM of the denominators of rational numbers inside the brackets.
    LCM of 11 and 5 = 55
    On multiplying fraction numerator negative 7 over denominator 11 end fraction with 5, we get fraction numerator negative 7 cross times 5 over denominator 11 cross times 5 end fraction equals fraction numerator negative 35 over denominator 55 end fraction
    On multiplying fraction numerator negative 2 over denominator 5 end fraction with 11, we get fraction numerator negative 2 cross times 11 over denominator 5 cross times 11 end fraction equals fraction numerator negative 22 over denominator 55 end fraction
    On adding, we get fraction numerator negative 35 over denominator 55 end fraction plus fraction numerator negative 22 over denominator 55 end fraction equals fraction numerator negative 57 over denominator 55 end fraction
    On substituting this in (i), we get fraction numerator negative 57 over denominator 55 end fraction plus fraction numerator negative 13 over denominator 22 end fraction
    Determine the LCM of the denominators of rational numbers.
    LCM of 55 and 22 = 110
    On multiplying fraction numerator negative 57 over denominator 55 end fraction with 2, we get fraction numerator negative 57 cross times 2 over denominator 55 cross times 2 end fraction equals fraction numerator negative 114 over denominator 110 end fraction
    On multiplying fraction numerator negative 13 over denominator 22 end fraction with 5, we get fraction numerator negative 13 cross times 5 over denominator 22 cross times 5 end fraction equals fraction numerator negative 65 over denominator 110 end fraction
    On adding, we get fraction numerator negative 114 over denominator 110 end fraction plus fraction numerator negative 65 over denominator 110 end fraction equals fraction numerator negative 179 over denominator 110 end fraction
    Thus we have LHS to be open parentheses fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator negative 2 over denominator 5 end fraction close parentheses plus fraction numerator negative 13 over denominator 22 end fraction equals fraction numerator negative 179 over denominator 110 end fraction
    Consider the RHS part, we have fraction numerator negative 7 over denominator 11 end fraction plus open parentheses fraction numerator negative 2 over denominator 5 end fraction plus fraction numerator negative 13 over denominator 22 end fraction close parentheses…(ii)
    Determine the LCM of the denominators of rational numbers inside the brackets.
    LCM of 5 and 22 = 110
    On multiplying fraction numerator negative 2 over denominator 5 end fraction with 22, we get fraction numerator negative 2 cross times 22 over denominator 5 cross times 22 end fraction equals fraction numerator negative 44 over denominator 110 end fraction
    On multiplying fraction numerator negative 13 over denominator 22 end fraction with 5, we get fraction numerator negative 13 cross times 5 over denominator 22 cross times 5 end fraction equals fraction numerator negative 65 over denominator 110 end fraction
    On adding, we get fraction numerator negative 44 over denominator 110 end fraction plus fraction numerator negative 65 over denominator 110 end fraction equals fraction numerator negative 109 over denominator 110 end fraction
    On substituting this in (ii), we get fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator negative 109 over denominator 110 end fraction
    Determine the LCM of the denominators of rational numbers.
    LCM of 11 and 110 = 110
    On multiplying fraction numerator negative 7 over denominator 11 end fraction with 10, we get fraction numerator negative 7 cross times 10 over denominator 11 cross times 10 end fraction equals fraction numerator negative 70 over denominator 110 end fraction
    On multiplying fraction numerator negative 109 over denominator 110 end fraction with 1, we get fraction numerator negative 109 cross times 1 over denominator 110 cross times 1 end fraction equals fraction numerator negative 109 over denominator 110 end fraction
    On adding, we get fraction numerator negative 70 over denominator 110 end fraction plus fraction numerator negative 109 over denominator 110 end fraction equals fraction numerator negative 179 over denominator 110 end fraction
    Thus we have RHS to be fraction numerator negative 7 over denominator 11 end fraction plus open parentheses fraction numerator negative 2 over denominator 5 end fraction plus fraction numerator negative 13 over denominator 22 end fraction close parentheses equals fraction numerator negative 179 over denominator 110 end fraction
    So we get LHS = RHS = fraction numerator negative 179 over denominator 110 end fraction
    Hence verified.

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