Question

how would you simplify... 6/(x+h) - 6/x

Answer 1

If all of it is over h

Answer 2

\[\frac{ \frac{ 6 }{ x + h } - \frac{ 6 }{ x } }{ h }\]Make the denominators the same in the upper term:\[\frac{ \frac{ 6 x }{ x(x + h) } - \frac{ 6 (x + h) }{ x (x + h) } }{ h } = \frac{ \frac{ 6 x - 6 (x + h) }{ x(x + h) } }{ h }\]Simplify: \[\frac{ \frac{ 6 x - 6x - 6h }{ x(x + h) } }{ h } = \frac{ \frac{ - 6h }{ x(x + h) } }{ h }\]Divide by h and simplify:
\[\frac{- 6h }{ hx(x + h) } = \frac{- 6 }{ x ^{2} + hx }\]