What is expand (mgr=mgh+(mgh)/2)*1/(mg) ?

The solution to expand (mgr=mgh+(mgh)/2)*1/(mg) is r=mgh+h/2

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expand (mgr=mgh+(mgh)/2)*1/(mg)

expand

(m g r = m g h + \frac{m g h}{2}) \cdot \frac{1}{m g}

r = m g h + \frac{h}{2}

Solution steps

(m g r = m g h + \frac{m g h}{2}) \frac{1}{m g}

= \frac{1}{m g} (= mm gg h r + \frac{m g h}{2})

Apply the distributive law:

a (b + c) = ab + a c

a = \frac{1}{m g}, b = m g r = m g h, c = \frac{m g h}{2}

\frac{1}{m g} m g r = m g h + \frac{1}{m g} \cdot \frac{m g h}{2}

m g \frac{1}{m g} r = m g h + \frac{1}{m g} \cdot \frac{m g h}{2}

Simplify

m g \frac{1}{m g} r = m g h + \frac{1}{m g} \cdot \frac{m g h}{2} : r = m g h + \frac{h}{2}

r = m g h + \frac{h}{2}

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What is expand (mgr=mgh+(mgh)/2)*1/(mg) ?
The solution to expand (mgr=mgh+(mgh)/2)*1/(mg) is r=mgh+h/2