Solve (a+b)^2*(a-b)^-5/(a+b)^3*(a-b)^-4

$$\frac { ( a + b ) ^ { 2 } \cdot ( a - b ) ^ { - 5 } } { ( a + b ) ^ { 3 } \cdot ( a - b ) ^ { - 4 } }$$

Evaluate

$$\frac{1}{a^{2}-b^{2}}$$

Solution Steps

Cancel out \left(a+b\right)^{2} in both numerator and denominator.

$$\frac{\left(a-b\right)^{-5}}{\left(a-b\right)^{-4}\left(a+b\right)}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{1}{\left(a+b\right)\left(a-b\right)^{1}}$$

Calculate a-b to the power of 1 and get a-b.

$$\frac{1}{\left(a+b\right)\left(a-b\right)}$$

Consider \left(a+b\right)\left(a-b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{1}{a^{2}-b^{2}}$$

Expand

$$\frac{1}{a^{2}-b^{2}}$$

Solution Steps

Cancel out \left(a+b\right)^{2} in both numerator and denominator.

$$\frac{\left(a-b\right)^{-5}}{\left(a-b\right)^{-4}\left(a+b\right)}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{1}{\left(a+b\right)\left(a-b\right)^{1}}$$

Calculate a-b to the power of 1 and get a-b.

$$\frac{1}{\left(a+b\right)\left(a-b\right)}$$

Consider \left(a+b\right)\left(a-b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{1}{a^{2}-b^{2}}$$