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

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

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simplify 1/((x+h)^2)-1/(x^2)

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

\frac{x ^{2} y}{4 x y} \cdot \frac{x}{6} \cdot \frac{3 y ^{5}}{x ^{4}}

z = \frac{- 1}{2} + \frac{1}{2} i

(x - 2) (x - 3) = 2

\frac{( x ^{2} - 2 x + 3 )}{x - 1}

(x - 2)^{2} < x (x - 4) + 8

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