Exercise
$\frac{\left(x+a\right)^{-2}-x^{-2}}{a}$
Step-by-step Solution
Learn how to solve problems step by step online. Simplify the expression ((x+a)^(-2)-x^(-2))/a. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Combine \frac{1}{\left(x+a\right)^{2}}+\frac{-1}{x^{2}} in a single fraction. Combine -1+\frac{x^{2}}{\left(x+a\right)^{2}} in a single fraction. Divide fractions \frac{\frac{\frac{x^{2}-\left(x+a\right)^{2}}{\left(x+a\right)^{2}}}{x^{2}}}{a} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.
Simplify the expression ((x+a)^(-2)-x^(-2))/a
Final answer to the exercise
$\frac{-2xa-a^{2}}{\left(x+a\right)^{2}x^{2}a}$