What is a/(a-b)-(2ab)/(a^2-b^2) ?

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

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simplify a/(a-b)-(2ab)/(a^2-b^2)

simplify

\frac{a}{a - b} - \frac{2 ab}{a ^{2} - b ^{2}}

\frac{a}{a + b}

Solution steps

\frac{a}{a - b} - \frac{2 ab}{a ^{2} - b ^{2}}

Least Common Multiplier of

a - b, a^{2} - b^{2} : (a - b) (a^{2} - b^{2})

Adjust Fractions based on the LCM

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

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

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

Simplify

a (a^{2} - b^{2}) - 2 ab (a - b) : a^{3} + a b^{2} - 2 a^{2} b

= \frac{a ^{3} + a b ^{2} - 2 a ^{2} b}{( a - b ) ( a ^{2} - b ^{2} )}

Cancel

\frac{a ^{3} + a b ^{2} - 2 a ^{2} b}{( a - b ) ( a ^{2} - b ^{2} )} : \frac{a}{a + b}

= \frac{a}{a + b}

- 4 (x - 3) \geq 2 x + 5

6 (2 x - 1)^{2} + 2 = - 7 (2 x - 1)

6 (x + 4) + 1 = x + 5

x^{2} - 4 x y - 77 y^{2}

\frac{16 m ^{4} - 81 n ^{4}}{2 m - 3 n}

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