What is (1/(a+b))(1/(b-a))-(1/(a-b))(1/(b-a)) ?

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

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simplify (1/(a+b))(1/(b-a))-(1/(a-b))(1/(b-a))

simplify

(\frac{1}{a + b}) (\frac{1}{b - a}) - (\frac{1}{a - b}) (\frac{1}{b - a})

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

Solution steps

(\frac{1}{a + b}) (\frac{1}{b - a}) - (\frac{1}{a - b}) (\frac{1}{b - a})

Simplify

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

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

\frac{1}{a + b} \cdot \frac{1}{b - a} = \frac{1}{( a + b ) ( b - a )}

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

= \frac{1}{( a + b ) ( b - a )} - \frac{1}{( a - b ) ( b - a )}

Simplify

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

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

Apply rule:

a - (- b) = a + b

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

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

(5 x + y)^{3}

10 c^{2} - 11 c^{9}

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

x^{2} \cdot (\frac{x}{y} - \frac{y}{x}) (\frac{y}{x} + \frac{x}{y}) \cdot y^{2}

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

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