What is 1/((x-5))-1/((x-3))+1/((x+5))-1/((x+3)) ?

The solution to 1/((x-5))-1/((x-3))+1/((x+5))-1/((x+3)) is (32x)/((x-5)(x-3)(x+5)(x+3))

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simplify 1/((x-5))-1/((x-3))+1/((x+5))-1/((x+3))

simplify

\frac{1}{( x - 5 )} - \frac{1}{( x - 3 )} + \frac{1}{( x + 5 )} - \frac{1}{( x + 3 )}

\frac{32 x}{( x - 5 ) ( x - 3 ) ( x + 5 ) ( x + 3 )}

Solution steps

\frac{1}{x - 5} - \frac{1}{x - 3} + \frac{1}{x + 5} - \frac{1}{x + 3}

Least Common Multiplier of

x - 5, x - 3, x + 5, x + 3 : (x - 5) (x - 3) (x + 5) (x + 3)

Adjust Fractions based on the LCM

= \frac{( x - 3 ) ( x + 5 ) ( x + 3 )}{( x - 5 ) ( x - 3 ) ( x + 5 ) ( x + 3 )} - \frac{( x - 5 ) ( x + 5 ) ( x + 3 )}{( x - 5 ) ( x - 3 ) ( x + 5 ) ( x + 3 )} + \frac{( x - 5 ) ( x - 3 ) ( x + 3 )}{( x - 5 ) ( x - 3 ) ( x + 5 ) ( x + 3 )} - \frac{( x - 5 ) ( x - 3 ) ( x + 5 )}{( x - 5 ) ( x - 3 ) ( x + 5 ) ( x + 3 )}

Apply the fraction rule:

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

= \frac{( x - 3 ) ( x + 5 ) ( x + 3 ) - ( x - 5 ) ( x + 5 ) ( x + 3 ) + ( x - 5 ) ( x - 3 ) ( x + 3 ) - ( x - 5 ) ( x - 3 ) ( x + 5 )}{( x - 5 ) ( x - 3 ) ( x + 5 ) ( x + 3 )}

Simplify

(x - 3) (x + 5) (x + 3) - (x - 5) (x + 5) (x + 3) + (x - 5) (x - 3) (x + 3) - (x - 5) (x - 3) (x + 5) : 32 x

= \frac{32 x}{( x - 5 ) ( x - 3 ) ( x + 5 ) ( x + 3 )}

(y^{2} z)^{3}

- x^{5} - 243

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

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

2 x^{3} + 5 x^{2} + 15 x + 18

What is 1/((x-5))-1/((x-3))+1/((x+5))-1/((x+3)) ?
The solution to 1/((x-5))-1/((x-3))+1/((x+5))-1/((x+3)) is (32x)/((x-5)(x-3)(x+5)(x+3))