What is (a+x)/(a-x)-(a-x)/(a+x) ?

The solution to (a+x)/(a-x)-(a-x)/(a+x) is (4ax)/((-x+a)(x+a))

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simplify (a+x)/(a-x)-(a-x)/(a+x)

simplify

\frac{a + x}{a - x} - \frac{a - x}{a + x}

\frac{4 a x}{( - x + a ) ( x + a )}

Solution steps

\frac{a + x}{a - x} - \frac{a - x}{a + x}

Least Common Multiplier of

a - x, a + x : (- x + a) (x + a)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(a + x)^{2} - (a - x)^{2} : 4 a x

= \frac{4 a x}{( - x + a ) ( x + a )}

v^{19}

2 x (3 x + 1)

\frac{x}{x ^{3}}

- x^{2} + 12 x - 11

\frac{( 3 x ^{2} - 13 x - 10 )}{( x - 5 )}

What is (a+x)/(a-x)-(a-x)/(a+x) ?
The solution to (a+x)/(a-x)-(a-x)/(a+x) is (4ax)/((-x+a)(x+a))