Exercise
$\left(x^{-1}+y^{-1}\right)\left(x^{-1}-y^{-1}\right)$
Step-by-step Solution
Learn how to solve factor by difference of squares problems step by step online. Simplify the product of conjugate binomials (x^(-1)+y^(-1))(x^(-1)-y^(-1)). The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Simplify \left(x^{-1}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals -1 and n equals 2. Simplify \left(y^{-1}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals -1 and n equals 2. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.
Simplify the product of conjugate binomials (x^(-1)+y^(-1))(x^(-1)-y^(-1))
Final answer to the exercise
$\frac{y^{2}-x^{2}}{x^{2}y^{2}}$