What is expand (sqrt((x+h)^2+1)-sqrt(x^2+1))/h ?

The solution to expand (sqrt((x+h)^2+1)-sqrt(x^2+1))/h is (sqrt(x^2+2xh+h^2+1))/h-(sqrt(x^2+1))/h

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expand (sqrt((x+h)^2+1)-sqrt(x^2+1))/h

expand

\frac{( x + h ) ^{2} + 1 - x ^{2} + 1}{h}

\frac{x ^{2} + 2 x h + h ^{2} + 1}{h} - \frac{x ^{2} + 1}{h}

Solution steps

\frac{( x + h ) ^{2} + 1 - x ^{2} + 1}{h}

Expand

(x + h)^{2} + 1 : x^{2} + 2 x h + h^{2} + 1

= \frac{x ^{2} + 2 x h + h ^{2} + 1 - x ^{2} + 1}{h}

Apply the fraction rule:

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

\frac{x ^{2} + 2 x h + h ^{2} + 1 - x ^{2} + 1}{h} = \frac{x ^{2} + 2 x h + h ^{2} + 1}{h} - \frac{x ^{2} + 1}{h}

= \frac{x ^{2} + 2 x h + h ^{2} + 1}{h} - \frac{x ^{2} + 1}{h}

(x - \frac{1}{x})^{3}

x (x^{5} e^{11 x} + 2)

\frac{1}{3} + \frac{2}{9} (0.8 - 1)

(2 n)!

What is expand (sqrt((x+h)^2+1)-sqrt(x^2+1))/h ?
The solution to expand (sqrt((x+h)^2+1)-sqrt(x^2+1))/h is (sqrt(x^2+2xh+h^2+1))/h-(sqrt(x^2+1))/h