What is sqrt((a-b)/((a-b)^2)*(a+b)/(a^2-b^2)) ?

The solution to sqrt((a-b)/((a-b)^2)*(a+b)/(a^2-b^2)) is 1/(a-b)

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simplify sqrt((a-b)/((a-b)^2)*(a+b)/(a^2-b^2))

simplify

\frac{a - b}{( a - b ) ^{2}} \cdot \frac{a + b}{a ^{2} - b ^{2}}

\frac{1}{a - b}

Solution steps

\frac{a - b}{( a - b ) ^{2}} \cdot \frac{a + b}{a ^{2} - b ^{2}}

\frac{a - b}{( a - b ) ^{2}} = \frac{1}{a - b}

= \frac{1}{a - b} \cdot \frac{a + b}{a ^{2} - b ^{2}}

\frac{a + b}{a ^{2} - b ^{2}} = \frac{1}{a - b}

= \frac{1}{a - b} \cdot \frac{1}{a - b}

Multiply

\frac{1}{a - b} \cdot \frac{1}{a - b} : \frac{1}{( a - b ) ^{2}}

= \frac{1}{( a - b ) ^{2}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{1}{( a - b ) ^{2}}

Apply radical rule:

assuming

a \geq 0

(a - b)^{2} = a - b

= \frac{1}{a - b}

Apply rule

1 = 1

= \frac{1}{a - b}

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What is sqrt((a-b)/((a-b)^2)*(a+b)/(a^2-b^2)) ?
The solution to sqrt((a-b)/((a-b)^2)*(a+b)/(a^2-b^2)) is 1/(a-b)