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}

e^{2 x} (2 x + 1)

(2 x - 3 y^{2}) d x

(x + i y)^{2} - 1

lo g_{9} \frac{9 x ^{7}}{y}

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

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