Basic algebra/fractions: derivationHow do I do this derivation step? I don't understand why there is equality. The derivation is from my textbook. m g − m ( g 1 + M 2 m ) = m g 1 + 2 m M

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Basic algebra/fractions: derivationHow do I do this derivation step? I don&#039;t understand why there is equality. The derivation is from my textbook.  m  g  −  m      (          g              1        +                  M                      2            m                                )    =            m      g              1      +                        2          m                M

Aibling6n2re · Accepted Answer

Have you tried writing it out?      m    g    −    m          (              g                  1          +          M                      /                    2          m                    )        =                  m        g        (        1        +        M                  /                2        m        )        −        m        g                    1        +        M                  /                2        m              =          M              2        m                            m        g                    1        +        M                  /                2        m              =    M                  m        g                    2        m        +        M              =         .    .    .  Yes?

Spencer Lutz · Accepted Answer

Trying to get:  m  g  −  m      (          g              1        +        M                  /                2        m              )    =            m      g              1      +      2      m              /            M      first factor out the m and g:  m  g      (    1    −          1              1        +                  M                      2            m                                )  Need the same denominator to add fractions  m  g      (                  1        +                  M                      2            m                                      1        +                  M                      2            m                                −          1              1        +                  M                      2            m                                )  Subtract now and the ones cancel in the numerator.  m  g      (                  M                  2          m                            1        +                  M                      2            m                                )  which is the same as  m  g      (          1                                    2            m                    M                          (          1          +                      M                          2              m                                )                      )  Multiply through on the denominator and the       M          2      m       cancels when multiplied with             2      m        M   but you also have to multiply the 1 by the term so:  m  g      (          1                                    2            m                    M                          (          1          +                      M                          2              m                                )                      )    =            m      g              1      +      2      m              /            M

Basic algebra/fractions: derivation How do I do this derivation step? I don't understand why there

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