Question

How come we can turn (((1 / (x + h)) - (1 / x)) / h) into ((1 / h) * ((x - (x + h)) / (x + h) * x)) I don't understand the steps in between the two.

Answer 1

The question is why \[\frac{ \frac{ 1 }{ x+h } + \frac{ 1 }{ x } }{ h } = \frac{ 1 }{ h } * \left[ \frac{ x - (x+h) }{ (x+h) * x } \right] \]
Answer:
\[\frac{ \frac{ 1 }{ x+h } - \frac{ 1 }{ x } }{ h }
= \frac { 1 }{ h } * \left[ \frac{ 1 }{ x+h } - \frac{ 1 }{ x } \right] \\
= \frac { 1 }{ h } * \left[ \frac{ 1 * x }{ (x+h) * x } - \frac{ 1* (x+h) }{ x * (x+h) } \right] \\
= \frac { 1 }{ h } * \left[ \frac{ x }{ (x+h) * x } - \frac{ (x+h) }{ (x+h) * x } \right] \\
= \frac { 1 }{ h } * \left[ \frac{ x - (x+h) }{ (x+h) * x } \right]\]

Answer 2

Thanks.