Prove equivalent fractions with ± signIf λ = n 1 n 2 = m 1 m 2 prove that λ = n 1 ± m 1 n 2 ± m 2 I know this is true if I add numbers to it 1 2 = 2 4 1 + 2 2 + 4 = 3 6 = 1 2 1 − 2 2 − 4 = − 1 − 2 = 1 2

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Prove equivalent fractions with   ± signIf  λ  =            n              1                    n              2              =            m              1                    m              2            prove that  λ  =                    n                  1                    ±              m                  1                                    n                  2                    ±              m                  2                    I know this is true if I add numbers to it      1    2    =      2    4              1      +      2              2      +      4        =      3    6    =      1    2              1      −      2              2      −      4        =            −      1              −      2        =      1    2

eishale2n · Accepted Answer

Compute the difference: From             n      1              n      2        =            m      1              m      2      , we know tha tthe numerator of            n      1              n      2        −            m      1              m      2        =                    n        1                    m        2            −              n        2                    m        1                            n        2                    m        2            is zero. Hence                                                        n              1                        ±                          m              1                                                          n              2                        ±                          m              2                                      −                              n            1                                n            2                                              =                              (                          n              1                        ±                          m              1                        )                          n              2                        −                          n              1                        (                          n              2                        ±                          m              2                        )                                (                          n              2                        ±                          m              2                        )                          m              1                                                                        =                                            n              1                                      n              2                        ±                          m              1                                      n              2                        −                          n              1                                      n              2                        ∓                          n              1                                      m              2                                            (                          n              2                        ±                          m              2                        )                          m              1                                                                        =                              ±            (                          n              1                                      m              2                        −                          n              2                                      m              1                        )                                (                          n              2                        ±                          m              2                        )                          m              1                                                                        =        0

Baladdaa9 · Accepted Answer

λ    =            n              1                    n              2              =            m              1                    m              2                →        n    1    =  λ  .      n    2          m    1    =  λ  .      m    2  so                              n          1                +                  m          1                                      n          2                +                  m          2                      =                    (        λ        .                  n          2                )        +        (        λ        .                  m          2                )                              n          2                +                  m          2                      =    λ                    (                  n          2                )        +        (                  m          2                )                              n          2                +                  m          2                      =  λ  .1  =  λalso for                               n          1                −                  m          1                                      n          2                −                  m          2                      =                    (        λ        .                  n          2                )        −        (        λ        .                  m          2                )                              n          2                −                  m          2                      =    λ                    (                  n          2                )        −        (                  m          2                )                              n          2                −                  m          2                      =  λ  .1  =  λ

If lambda=(n_(1))/(n_(2))=(m_(1))/(m_(2)) prove that lambda=(n_(1)+-m_(1))/(n_2+-m_2) I know this is true if I add numbers to it 1/2=2/4 *(1+2)/(2+4)=3/6=1/2 (1−2)/(2−4)=(−1)/(−2)=1/2

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