What is h+1/(x+h)-1/x ?

The solution to h+1/(x+h)-1/x is (h^2x+hx^2-h)/(x(h+x))

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simplify h+1/(x+h)-1/x

simplify

h + \frac{1}{x + h} - \frac{1}{x}

\frac{h ^{2} x + h x ^{2} - h}{x ( h + x )}

Solution steps

h + \frac{1}{x + h} - \frac{1}{x}

Join

\frac{1}{x + h} - \frac{1}{x} : \frac{x - ( h + x )}{x ( h + x )}

= h + \frac{x - ( h + x )}{x ( h + x )}

Apply the fraction rule:

a + \frac{b}{c} = \frac{a c + b}{c}

= \frac{h x ( h + x ) + x - ( h + x )}{x ( h + x )}

Simplify

h x (h + x) + x - (h + x) : h^{2} x + h x^{2} - h

= \frac{h ^{2} x + h x ^{2} - h}{x ( h + x )}

(- 2 + 5 i)^{2}

(1 0^{- 1})^{2}

\frac{3 - 3}{3}

\frac{5}{4} \times 3

+ \frac{20 π}{15}